Theorem nebi

Description: Contraposition law for inequality. (Contributed by NM, 28-Dec-2008)

	Ref	Expression
Assertion	nebi	|- ( ( A = B <-> C = D ) <-> ( A =/= B <-> C =/= D ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ( A = B <-> C = D ) -> ( A = B <-> C = D ) )
2	1	necon3bid	|- ( ( A = B <-> C = D ) -> ( A =/= B <-> C =/= D ) )
3		id	|- ( ( A =/= B <-> C =/= D ) -> ( A =/= B <-> C =/= D ) )
4	3	necon4bid	|- ( ( A =/= B <-> C =/= D ) -> ( A = B <-> C = D ) )
5	2 4	impbii	|- ( ( A = B <-> C = D ) <-> ( A =/= B <-> C =/= D ) )