Theorem neanior

Description: A De Morgan's law for inequality. (Contributed by NM, 18-May-2007)

	Ref	Expression
Assertion	neanior	|- ( ( A =/= B /\ C =/= D ) <-> -. ( A = B \/ C = D ) )

Proof

Step	Hyp	Ref	Expression
1		df-ne	|- ( A =/= B <-> -. A = B )
2		df-ne	|- ( C =/= D <-> -. C = D )
3	1 2	anbi12i	|- ( ( A =/= B /\ C =/= D ) <-> ( -. A = B /\ -. C = D ) )
4		pm4.56	|- ( ( -. A = B /\ -. C = D ) <-> -. ( A = B \/ C = D ) )
5	3 4	bitri	|- ( ( A =/= B /\ C =/= D ) <-> -. ( A = B \/ C = D ) )