Theorem neorian

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

	Ref	Expression
Assertion	neorian	|- ( ( 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	orbi12i	|- ( ( A =/= B \/ C =/= D ) <-> ( -. A = B \/ -. C = D ) )
4		ianor	|- ( -. ( A = B /\ C = D ) <-> ( -. A = B \/ -. C = D ) )
5	3 4	bitr4i	|- ( ( A =/= B \/ C =/= D ) <-> -. ( A = B /\ C = D ) )