Theorem necon2d

Description: Contrapositive inference for inequality. (Contributed by NM, 28-Dec-2008)

	Ref	Expression
Hypothesis	necon2d.1	|- ( ph -> ( A = B -> C =/= D ) )
Assertion	necon2d	|- ( ph -> ( C = D -> A =/= B ) )

Proof

Step	Hyp	Ref	Expression
1		necon2d.1	|- ( ph -> ( A = B -> C =/= D ) )
2		df-ne	|- ( C =/= D <-> -. C = D )
3	1 2	imbitrdi	|- ( ph -> ( A = B -> -. C = D ) )
4	3	necon2ad	|- ( ph -> ( C = D -> A =/= B ) )