Editing Conditional proof (section)

==Overview==
The assumed antecedent of a conditional proof is called the '''conditional proof assumption'''<!--boldface per WP:R#PLA--> ('''CPA'''). Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion [[Logical consequence|necessarily follows]]. The validity of a conditional proof does not require that the CPA be true, only that ''if it were true'' it would lead to the consequent.

Conditional proofs are of great importance in [[mathematics]]. Conditional proofs exist linking several otherwise unproven [[conjecture]]s, so that a proof of one conjecture may immediately imply the validity of several others. It can be much easier to show a proposition's truth to follow from another proposition than to prove it independently.

A famous network of conditional proofs is the [[NP-complete]] class of complexity theory. There is a large number of interesting tasks (see ''[[List of NP-complete problems]]''), and while it is not known if a polynomial-time solution exists for any of them, it is known that if such a solution exists for some of them, one exists for all of them. Similarly, the [[Riemann hypothesis]] has many consequences already proven.