Theorem necon1abii 1619

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon1abii.1	|- (-. ph <-> A = B)

Assertion

Ref	Expression
necon1abii	|- (A =/= B <-> ph)

Proof of Theorem necon1abii

Step	Hyp	Ref	Expression
1		df-ne 1590	. 2 |- (A =/= B <-> -. A = B)
2		necon1abii.1	. . 3 |- (-. ph <-> A = B)
3	2	con1bii 220	. 2 |- (-. A = B <-> ph)
4	1, 3	bitr 173	1 |- (A =/= B <-> ph)

Syntax hints:  -. wn 2   <-> wb 146   = wceq 958   =/= wne 1588

This theorem is referenced by:  necon2abii 1623

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-ne 1590

Copyright terms: Public domain