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Theorem nesym 2265
Description: Characterization of inequality in terms of reversed equality (see bicom 132). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym  |-  ( A  =/=  B  <->  -.  B  =  A )

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2058 . 2  |-  ( A  =  B  <->  B  =  A )
21necon3abii 2256 1  |-  ( A  =/=  B  <->  -.  B  =  A )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 102    = wceq 1259    =/= wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-ne 2221
This theorem is referenced by:  nesymi  2266  nesymir  2267  0neqopab  5578  fzdifsuc  9045
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