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If anyone wants to believe in BOD, then the following conditions are the ONLY ones given by saints and Trent.

1.  St Thomas/St Bellarmine/St Augustine/ Trent ==  All of them talk about FORMAL CATECHUMENS.
2.  Trent's schema on justification is in the context of CATECHUMENS PREPARING FOR BAPTISM.

3.  St Thomas == specifically says that the minimum requirements for conversion are:
a.  Belief/acceptance of the Incarnation (i.e. Christ, as God, came to redeem the human race from Original Sin).
b.  Belief/acceptance of the Trinity.

4.  The Holy Office letter (in 1600s) to missionaries, on the conditions necessary for pagan indians to be baptized:
a.  Belief/acceptance of the Incarnation and Trinity.

5.  Trent gives multiple chapters on the conditions necessary for a catechumen to be baptized.  There is no way BOD applies to anyone other than catechumens.


Conclusions:
a.  Catechumen ==  a Christian convert under instruction before baptism.
b.  A muslim cannot be saved as a muslim, because the muslim religion denies the Incarnation/Trinity.
c.  Same applies for Jews, hindus, pagans, etc.
d.  All of these peoples would have to REJECT THEIR OLD RELIGIONS FIRST, which is a REQUIREMENT to being a catechumen.
e.  The reason why St Thomas/St Bellarmine/St Alphonsus argued that catechumens could receive BOD is because they were already "spiritually united to the Church" by their desire to enter it.  Catechumens were called "christians" because they wanted to be such.
f.  No muslim, jew, pagan, etc can be "spiritually united" to the Church if they have not rejected their false religion first. 
g.  A muslim cannot come to a priest and say "I want to take lesson on becoming a catholic, but I still want to be muslim."  Uhhh...that doesn't work.
h.  You can't receive BOD if you don't have a desire (or knowledge) to be catholic first.  You cannot desire what you do not know. 

If you want to believe that BOD exists, then it ONLY exists for formal catechumens, who have rejected their old religions and desire to enter the Church.  And...they have the minimum knowledge necessary to desire the Church (i.e. knowledge/acceptance of the 2 minimum doctrines -- Incarnation/Trinity).

Anyone who does not fulfill these requirements 1) isn't a catechumen, 2) doesn't desire catholicism, 3) doesn't know enough to desire either.  You cannot desire what you do not know.

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Anyone who holds the position that ANYONE BESIDES CATECHUMENS could receive BOD is a heretic.  There is no support for your theories and they contradict St Thomas, St Augustine, St Alphonsus, St Bellarmine, and Trent.  Your theories are modernist, anti-catholic and have no basis in church history, theology or doctrine.

Apply that insanity to "One Lord, one faith" and it fails miserably. 

The content of the faith can be complete, incomplete, or corrupted.

Complete : it contains everything necessary for salvation, nothing more nothing less.

Incomplete : everything in those teachings is true, but they are incomplete. Example : Old Testament law before Christ came.

Corrupted : it contains some true statements and some false statements, believing in this leads to hell. Example : islam.