Theorem necon4abid 1629

Description: Contrapositive law deduction for inequality.

Hypothesis

Ref	Expression
necon4abid.1	|- (ph -> (A =/= B <-> -. ps))

Assertion

Ref	Expression
necon4abid	|- (ph -> (A = B <-> ps))

Proof of Theorem necon4abid

Step	Hyp	Ref	Expression
1		necon4abid.1	. . 3 |- (ph -> (A =/= B <-> -. ps))
2		df-ne 1587	. . 3 |- (A =/= B <-> -. A = B)
3	1, 2	syl5bbr 534	. 2 |- (ph -> (-. A = B <-> -. ps))
4	3	con4bid 524	1 |- (ph -> (A = B <-> ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   = wceq 956   =/= wne 1585

This theorem is referenced by:  nmounbi 8439

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-an 225  df-ne 1587

Copyright terms: Public domain