Theorem necon2bbid 1623

Description: Contrapositive deduction for inequality.

Hypothesis

Ref	Expression
necon2bbid.1	|- (ph -> (ps <-> A =/= B))

Assertion

Ref	Expression
necon2bbid	|- (ph -> (A = B <-> -. ps))

Proof of Theorem necon2bbid

Step	Hyp	Ref	Expression
1		necon2bbid.1	. . 3 |- (ph -> (ps <-> A =/= B))
2		df-ne 1587	. . 3 |- (A =/= B <-> -. A = B)
3	1, 2	syl6bb 536	. 2 |- (ph -> (ps <-> -. A = B))
4	3	con2bid 526	1 |- (ph -> (A = B <-> -. ps))

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

This theorem is referenced by:  necon4bid 1630  omwordi 4202  omass 4211  infxpidmlem10 7561

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

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