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Theorem necon3abii 2321
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 2286 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
2 necon3abii.1 . 2  |-  ( A  =  B  <->  ph )
31, 2xchbinx 656 1  |-  ( A  =/=  B  <->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104    = wceq 1316    =/= wne 2285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589
This theorem depends on definitions:  df-bi 116  df-ne 2286
This theorem is referenced by:  necon3bbii  2322  necon3bii  2323  nesym  2330  n0rf  3345  gcd0id  11594
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