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Theorem neneqad 2516
Description: If it is not the case that two classes are equal, they are unequal. Converse of neneqd 2462. One-way deduction form of df-ne 2448. (Contributed by David Moews, 28-Feb-2017.)
Hypothesis
Ref Expression
neneqad.1  |-  ( ph  ->  -.  A  =  B )
Assertion
Ref Expression
neneqad  |-  ( ph  ->  A  =/=  B )

Proof of Theorem neneqad
StepHypRef Expression
1 neneqad.1 . . 3  |-  ( ph  ->  -.  A  =  B )
21con2i 112 . 2  |-  ( A  =  B  ->  -.  ph )
32necon2ai 2491 1  |-  ( ph  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1623    =/= wne 2446
This theorem is referenced by:  chordthmlem  20129  xrge0neqmnf  23330  xrge0npcan  23333  logccne0  23397  stirlinglem5  27827  sigardiv  27851  sigarcol  27854  sharhght  27855
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 2448
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