Theorem necon3d

Description: Contrapositive law deduction for inequality. (Contributed by NM, 10-Jun-2006)

	Ref	Expression
Hypothesis	necon3d.1	|- ( ph -> ( A = B -> C = D ) )
Assertion	necon3d	|- ( ph -> ( C =/= D -> A =/= B ) )

Proof

Step	Hyp	Ref	Expression
1		necon3d.1	|- ( ph -> ( A = B -> C = D ) )
2	1	necon3ad	|- ( ph -> ( C =/= D -> -. A = B ) )
3		df-ne	|- ( A =/= B <-> -. A = B )
4	2 3	imbitrrdi	|- ( ph -> ( C =/= D -> A =/= B ) )