Theorem neanior 2601

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

Assertion

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

Proof of Theorem neanior

Step	Hyp	Ref	Expression
1		df-ne 2518	. . 3 |- (A =/= B <-> -. A = B)
2		df-ne 2518	. . 3 |- (C =/= D <-> -. C = D)
3	1, 2	anbi12i 678	. 2 |- ((A =/= B /\ C =/= D) <-> (-. A = B /\ -. C = D))
4		pm4.56 481	. 2 |- ((-. A = B /\ -. C = D) <-> -. (A = B \/ C = D))
5	3, 4	bitri 240	1 |- ((A =/= B /\ C =/= D) <-> -. (A = B \/ C = D))

Syntax hints:  -. wn 3   <-> wb 176   \/ wo 357   /\ wa 358   = wceq 1642   =/= wne 2516

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ne 2518

This theorem is referenced by:  nelpri  3754