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Theorem necon4bbid 2511
Description: Contrapositive law deduction for inequality. (Contributed by NM, 9-May-2012.)
Hypothesis
Ref Expression
necon4bbid.1  |-  ( ph  ->  ( -.  ps  <->  A  =/=  B ) )
Assertion
Ref Expression
necon4bbid  |-  ( ph  ->  ( ps  <->  A  =  B ) )

Proof of Theorem necon4bbid
StepHypRef Expression
1 necon4bbid.1 . . . 4  |-  ( ph  ->  ( -.  ps  <->  A  =/=  B ) )
21bicomd 192 . . 3  |-  ( ph  ->  ( A  =/=  B  <->  -. 
ps ) )
32necon4abid 2510 . 2  |-  ( ph  ->  ( A  =  B  <->  ps ) )
43bicomd 192 1  |-  ( ph  ->  ( ps  <->  A  =  B ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    = wceq 1623    =/= wne 2446
This theorem is referenced by:  fzn  10810  lgsqr  20585
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-ne 2448
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