Geremia - The use of the word "and" connecting the two tells you that the anathema applies when the two are combined.  If "or" connected the two, then you could say the anathema applies to them separately, but also equally.  

You are however onto something.  I thought over this same thing with regard to papal condemnations of erroneous sentences and perhaps anathemas like this.  And, I can recall, but cannot give an example at the moment, that some condemned sentences of heretics had ideas in them that were not in themselves erroneous or warranting of a condemnation.  But, attached to or combined with these ideas were clearly erroneous ideas that warranted a condemnation.  What is debatable is if it warrants a "wholesale" condemnation(baby with the bathwater).

Erroneous ideas would often use non erroneous ideas as a vehicle.  This was not like modernism where you have completely contradictory ideas combined.  But, error was combined with a permissible position.  But, none the less, in situations, the whole sentence and all ideas contained within were condemned.  However, that is not to say that the permissible idea is actually condemned.  Because, there is the "context" card trick that authorities have up their sleeve.  And, they use it.  However, that is imperfect.  And, I think it is a sloppy.  Canon Hesse even mentioned how there have been inconvenient or perhaps imprudent papal judgments/decisions made that had regrettable consequences later.  

While this is an interesting logical question, does the answer really matter?  If one states that "the marriage state is to be placed above the state of virginity, or of celibacy" isn't one necessarily also saying that "it is not better and more blessed to remain in virginity, or in celibacy, than to be united in matrimony"?

"The marriage state is to be placed above the state of virginity, or of celibacy" clearly means marriage is greater than virginity/celibacy.
"It is not better and more blessed to remain in virginity, or in celibacy, than to be united in matrimony" means matrimony and virginity/celibacy are at least on the same level.
Thus, these statements do not mean the same thing.

Take for example this dogma from the 24th Session of the Council of Trent:

Quote from: Canon X.

If any one saith, that the marriage state is to be placed above the state of virginity, or of celibacy, and that it is not better and more blessed to remain in virginity, or in celibacy, than to be united in matrimony: let him be anathema.

Suppose I break this into two parts:

Quote from: If anyone

the marriage state is to be placed above the state of virginity, or of celibacy

and

Quote

it is not better and more blessed to remain in virginity, or in celibacy, than to be united in matrimony

Is one only anathematized if he holds both of these statements, or if [is] he also anathematized if he holds either of them individually?

(This is a logic question dealing with "distribution": Does the "Si quis dixerit…anathema sit" distribute across the "et" joining these two clauses, or does it only apply to both clauses taken together?)

In answer to your question, it is not proper to separate this dogma into two different teachings, because it is one teaching, one dogma, with two aspects, both of which are descriptive of the whole.  We distinguish but we do not separate.  

(Incidentally, the word "saith" is pronounced SETH, not SAY-ith.)

The first part, "If any one saith, that the marriage state is to be placed above the state of virginity, or of celibacy," would be easily misunderstood by itself, since it is an incomplete description of the principle being condemned.

In what way would the marriage state be placed above virginity or celibacy?  Would it be for purposes of law or of eligibility to govern, like a prince or a king?  Could it refer to the validity of a pope, for example, or of sacerdotal ordination?  In our age we have pretty much lost the significance of kingship and queenship, but how about eligibility for trade recognition - could it mean that a married person would be more capable of receiving an Oscar than would a virgin or a celibate person?  

The first part only had "to be placed above" - but it does not say where this placement occurs.  Is it on a shelf?  Is it in some kind of hierarchy?  Does it refer to job status, like what level of management (office manager vs. regional manager)?  Or is it like the authority level of military office (staff sergeant or brigadier general).

Where you ask, "Is one only anathematized if he holds both of these statements, or [is] he also anathematized if he holds either of them individually?" -- as you can probably see now, it makes little sense to wonder which of the two statements could be anathematized, because the first is not clear enough to be comprehensible.  It requires the second statement to become understandable.

All manner of questions like this are answered by the second part of the dogma, which says, "and that it is not better and more blessed to remain in virginity, or in celibacy, than to be united in matrimony: let him be anathema."

Here, in addition to "be placed above" we have "better and more blessed."

The words "better and more blessed" are introduced only in this second part, which now makes clear that the meaning of this dogma is in reference to spiritual matters, and not merely temporal ones.  

This was written at a time when the Church had much more awareness and attentiveness to spiritual matters, compared to post Vat.II, when a nearly universal agenda is unleashed, one of relegating all manner of recognition to temporal matters to the exclusion of spiritual ones, as if to tacitly deny the existence of the latter.

.

By the way:
Against the dogma used as an example in the first post above, Amoris Lætitia §159. repeats John Paul II's Theology of the Body heresy that the state of virginity is not higher than that of marriage:

Reflecting on this, Saint John Paul II noted that the biblical texts “give no reason to assert the ‘inferiority’ of marriage, nor the ‘superiority’ of virginity or celibacy”166 based on sɛҳuąƖ abstinence. Rather than speak absolutely of the superiority of virginity, it should be enough to point out that the different states of life complement one another, and consequently that some can be more perfect in one way and others in another.

166. Catechesis (14 April 1982), 1: Insegnamenti V/1 (1982), 1176.