Metamath Proof Explorer


Theorem ifnefalse

Description: When values are unequal, but an "if" condition checks if they are equal, then the "false" branch results. This is a simple utility to provide a slight shortening and simplification of proofs versus applying iffalse directly in this case. It happens, e.g., in oevn0 . (Contributed by David A. Wheeler, 15-May-2015)

Ref Expression
Assertion ifnefalse ABifA=BCD=D

Proof

Step Hyp Ref Expression
1 df-ne AB¬A=B
2 iffalse ¬A=BifA=BCD=D
3 1 2 sylbi ABifA=BCD=D