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Theorem necon3abii 2285
Description: Deduction from equality to inequality. (Contributed by NM, 9-Nov-2007.)
Hypothesis
Ref Expression
necon3abii.1  |-  ( A  =  B  <->  ph )
Assertion
Ref Expression
necon3abii  |-  ( A  =/=  B  <->  -.  ph )

Proof of Theorem necon3abii
StepHypRef Expression
1 df-ne 2250 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
2 necon3abii.1 . 2  |-  ( A  =  B  <->  ph )
31, 2xchbinx 640 1  |-  ( A  =/=  B  <->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103    = wceq 1285    =/= wne 2249
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-ne 2250
This theorem is referenced by:  necon3bbii  2286  necon3bii  2287  nesym  2294  n0rf  3277  gcd0id  10561
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