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One place where supplied jurisdiction becomes a serious concern is regarding validity of absolution in the confessional.
A priest needs to have jurisdiction when hearing a penitent's confession, in order to absolve his sins.
The local Novus Ordo parish has this from the local bishop, so the priests' absolution is valid (presuming he's really a priest and that he intends to give absolution).
But independent priests and SSPX priests must rely on supplied jurisdiction, instead of ordinary jurisdiction, since they don't have the permission of the local bishop to hear confessions.
Someone might ask, "But how does an independent priest get supplied jurisdiction, from some docuмent or authority?" The answer is that whenever a Catholic asks a priest to hear his confession, at that moment, the priest receives ("is supplied with") the necessary jurisdiction, directly from God, through the Church, even without the Pope's consent, because the Pope has no power to prevent the Church's HIGHEST LAW (the salvation of souls) from being efficacious (salus animarum lex suprema ecclesia est).
And by extension, the fact that a person stands in line to confess in turn to an independent priest presumes the penitent is requesting absolution from that priest, such that jurisdiction is supplied to the priest each time a penitent kneels down and says, "Bless me, Father, for I have sinned; it's been ____ days since my last confession..."
It was informative to see, about 2 years ago, when +F threatened to deny ordained priests any jurisdiction, such that their absolutions would be nullified without +Fellay's approval -- as if he had presumed to have ordinary jurisdiction. In context, he was apparently speaking only to SSPX seminarians who were about to be ordained, and he was attempting to frighten them into submission insuring that they wouldn't dare to leave the SSPX after ordination, and become independent.
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