All proofs at least implicitly contain the conclusion in the assumptions or axioms. That’s because proofs don’t generate information, they just unravel what one has already assumed by definition or axioms.
So yes, I’m implicitly assuming the conclusion in the assumptions. The point of the proof was to convince people who agreed with all the assumptions in the first place but who did not believe in the conclusion. There are people who do believe the assumptions but do not agree with the conclusion, which, as you say is in the assumptions.
All proofs at least implicitly contain the conclusion in the assumptions or axioms. That’s because proofs don’t generate information, they just unravel what one has already assumed by definition or axioms.
So yes, I’m implicitly assuming the conclusion in the assumptions. The point of the proof was to convince people who agreed with all the assumptions in the first place but who did not believe in the conclusion. There are people who do believe the assumptions but do not agree with the conclusion, which, as you say is in the assumptions.