Theorem necon4bid

Description: Contrapositive law deduction for inequality. (Contributed by NM, 29-Jun-2007)

	Ref	Expression
Hypothesis	necon4bid.1	|- ( ph -> ( A =/= B <-> C =/= D ) )
Assertion	necon4bid	|- ( ph -> ( A = B <-> C = D ) )

Proof

Step	Hyp	Ref	Expression
1		necon4bid.1	|- ( ph -> ( A =/= B <-> C =/= D ) )
2	1	necon2bbid	|- ( ph -> ( C = D <-> -. A =/= B ) )
3		nne	|- ( -. A =/= B <-> A = B )
4	2 3	bitr2di	|- ( ph -> ( A = B <-> C = D ) )