Theorem neorian 2604

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

Assertion

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

Proof of Theorem neorian

Step	Hyp	Ref	Expression
1		df-ne 2519	. . 3 |- (A =/= B <-> -. A = B)
2		df-ne 2519	. . 3 |- (C =/= D <-> -. C = D)
3	1, 2	orbi12i 507	. 2 |- ((A =/= B \/ C =/= D) <-> (-. A = B \/ -. C = D))
4		ianor 474	. 2 |- (-. (A = B /\ C = D) <-> (-. A = B \/ -. C = D))
5	3, 4	bitr4i 243	1 |- ((A =/= B \/ C =/= D) <-> -. (A = B /\ C = D))

This proof depends on syntax axioms:  -. wn 3   <-> wb 176   \/ wo 357   /\ wa 358   = wceq 1642   =/= wne 2517

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ne 2519

This theorem is used by: (None)