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Theorem necon3abii 2628
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 2600 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
2 necon3abii.1 . 2  |-  ( A  =  B  <->  ph )
31, 2xchbinx 302 1  |-  ( A  =/=  B  <->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    = wceq 1652    =/= wne 2598
This theorem is referenced by:  necon3bbii  2629  necon3bii  2630  n0f  3628  rankxplim3  7794  rankxpsuc  7795  dflt2  10730  gcd0id  13011  ballotlemi1  24748  axlowdimlem13  25841  filnetlem4  26347  pellex  26835  dihatlat  31971
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 2600
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