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Theorem neneqad 2529
Description: If it is not the case that two classes are equal, they are unequal. Converse of neneqd 2475. One-way deduction form of df-ne 2461. (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 2504 1  |-  ( ph  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1632    =/= wne 2459
This theorem is referenced by:  chordthmlem  20145  xrge0neqmnf  23345  xrge0npcan  23348  logccne0  23412  stirlinglem5  27930  sigardiv  27954  sigarcol  27957  sharhght  27958
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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