Theorem necon2abii 2572

Description: Contrapositive inference for inequality. (Contributed by NM, 2-Mar-2007.)

Hypothesis

Ref	Expression
necon2abii.1	|- (A = B <-> -. ph)

Assertion

Ref	Expression
necon2abii	|- (ph <-> A =/= B)

Proof of Theorem necon2abii

Step	Hyp	Ref	Expression
1		necon2abii.1	. . . 4 |- (A = B <-> -. ph)
2	1	bicomi 193	. . 3 |- (-. ph <-> A = B)
3	2	necon1abii 2568	. 2 |- (A =/= B <-> ph)
4	3	bicomi 193	1 |- (ph <-> A =/= B)

Syntax hints:  -. wn 3   <-> wb 176   = wceq 1642   =/= wne 2517

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-ne 2519

This theorem is referenced by: (None)