Theorem necon3bii 2243

Description: Inference from equality to inequality. (Contributed by NM, 23-Feb-2005.)

Hypothesis

Ref	Expression
necon3bii.1	|- ( A = B <-> C = D )

Assertion

Ref	Expression
necon3bii	|- ( A =/= B <-> C =/= D )

Proof of Theorem necon3bii

Step	Hyp	Ref	Expression
1		necon3bii.1	. . 3 |- ( A = B <-> C = D )
2	1	necon3abii 2241	. 2 |- ( A =/= B <-> -. C = D )
3		df-ne 2206	. 2 |- ( C =/= D <-> -. C = D )
4	2, 3	bitr4i 176	1 |- ( A =/= B <-> C =/= D )

Syntax hints:   -. wn 3   <-> wb 98   = wceq 1243   =/= wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-ne 2206

This theorem is referenced by:  necom  2289  negne0bi  7284