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	|- ( A =/= B -> if ( A = B , C , D ) = D )

Proof

Step	Hyp	Ref	Expression
1		df-ne	|- ( A =/= B <-> -. A = B )
2		iffalse	|- ( -. A = B -> if ( A = B , C , D ) = D )
3	1 2	sylbi	|- ( A =/= B -> if ( A = B , C , D ) = D )