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Theorem necon2abii 2514
Description: Contrapositive inference for inequality. (Contributed by NM, 2-Mar-2007.)
Hypothesis
Ref Expression
necon2abii.1  |-  ( A  =  B  <->  -.  ph )
Assertion
Ref Expression
necon2abii  |-  ( ph  <->  A  =/=  B )

Proof of Theorem necon2abii
StepHypRef Expression
1 necon2abii.1 . . . 4  |-  ( A  =  B  <->  -.  ph )
21bicomi 193 . . 3  |-  ( -. 
ph 
<->  A  =  B )
32necon1abii 2510 . 2  |-  ( A  =/=  B  <->  ph )
43bicomi 193 1  |-  ( ph  <->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    = wceq 1632    =/= wne 2459
This theorem is referenced by:  flimsncls  17697  tsmsgsum  17837  wilthlem2  20323  locfindis  26408  elnev  27741
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 2461
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