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Theorem nesym 2353
Description: Characterization of inequality in terms of reversed equality (see bicom 139). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym  |-  ( A  =/=  B  <->  -.  B  =  A )

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2141 . 2  |-  ( A  =  B  <->  B  =  A )
21necon3abii 2344 1  |-  ( A  =/=  B  <->  -.  B  =  A )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104    = wceq 1331    =/= wne 2308
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 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-ne 2309
This theorem is referenced by:  nesymi  2354  nesymir  2355  0neqopab  5816  fzdifsuc  9868  isprm3  11805
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