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Theorem necon2bbii 2660
Description: Contrapositive inference for inequality. (Contributed by NM, 13-Apr-2007.)
Hypothesis
Ref Expression
necon2bbii.1  |-  ( ph  <->  A  =/=  B )
Assertion
Ref Expression
necon2bbii  |-  ( A  =  B  <->  -.  ph )

Proof of Theorem necon2bbii
StepHypRef Expression
1 necon2bbii.1 . . . 4  |-  ( ph  <->  A  =/=  B )
21bicomi 194 . . 3  |-  ( A  =/=  B  <->  ph )
32necon1bbii 2656 . 2  |-  ( -. 
ph 
<->  A  =  B )
43bicomi 194 1  |-  ( A  =  B  <->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    = wceq 1652    =/= wne 2599
This theorem is referenced by:  xpeq0  5293  dmsn0  5337  disjex  24032  disjexc  24033
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 178  df-ne 2601
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