Theorem necon3bbid 1597

Description: Deduction from equality to inequality.

Hypothesis

Ref	Expression
necon3bbid.1	|- (ph -> (ps <-> A = B))

Assertion

Ref	Expression
necon3bbid	|- (ph -> (-. ps <-> A =/= B))

Proof of Theorem necon3bbid

Step	Hyp	Ref	Expression
1		necon3bbid.1	. . . 4 |- (ph -> (ps <-> A = B))
2	1	bicomd 520	. . 3 |- (ph -> (A = B <-> ps))
3	2	necon3abid 1596	. 2 |- (ph -> (A =/= B <-> -. ps))
4	3	bicomd 520	1 |- (ph -> (-. ps <-> A =/= B))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   = wceq 954   =/= wne 1582

This theorem is referenced by:  eldifsn 2458  php 4499  norm1ex 9061  lnfncon 9928

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 1584

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