Using a conjecture to solve a conjecture Is it mathematically correct to use a conjecture to prove another conjecture ? And if the second one is proved, does that mean that we'll only focus on proving the first ? There are many cases that emerge from this.
This idea came to my mind while studying Goldbach's Conjecture
 A: A mathematical theorem is typically a statement $P\implies Q$ that is logically true under the theory's axioms.
A conjecture is an unproven theorem.
Consider the following valid mathematical proof:
    $P\quad$  and $\quad P\implies (A\implies B);$
    therefore $\quad A\implies B.$
The first line contain the assumptions (also called premises or hypotheses), while the second line contains the conclusion.

*

*If we know $P$ to be true, and $\big[P\implies (A\implies B)\big]$ to
be a theorem, then we can rightly consider $\big[A\implies B\big]$ to
be another theorem. In this case, the above proof is a sound
argument.


*On the other hand, if we know $P$ to be true, but $\big[P\implies
   (A\implies B)\big]$ is merely a conjecture, then $\big[A\implies
   B\big]$ has to be another conjecture.

*

*If the first conjecture becomes proven, then we're back to the
previous case, and the second conjecture automatically too becomes
proven.

*But if the first conjecture becomes disproven, then the above proof,
while still valid, becomes unsound, and the second conjecture
remains a conjecture. (Even though the second conjecture had been
derived from the first, disproving the latter does not automatically
disprove the former.)



