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Theorem necon2bbii 2698
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 205 . . 3  |-  ( A  =/=  B  <->  ph )
32necon1bbii 2695 . 2  |-  ( -. 
ph 
<->  A  =  B )
43bicomi 205 1  |-  ( A  =  B  <->  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    = wceq 1437    =/= wne 2625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-ne 2627
This theorem is referenced by:  xpeq0  5277  dmsn0  5323  disjex  28041  disjexc  28042  suppss3  28155
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