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Theorem neneqad 2334
Description: If it is not the case that two classes are equal, they are unequal. Converse of neneqd 2276. One-way deduction form of df-ne 2256. (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 592 . 2  |-  ( A  =  B  ->  -.  ph )
32necon2ai 2309 1  |-  ( ph  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1289    =/= wne 2255
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 579  ax-in2 580
This theorem depends on definitions:  df-bi 115  df-ne 2256
This theorem is referenced by:  ne0i  3292  nsuceq0g  4243  fidifsnen  6576  nqnq0pi  6987  xrlttri3  9257
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