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Theorem nesym 2300
Description: Characterization of inequality in terms of reversed equality (see bicom 138). (Contributed by BJ, 7-Jul-2018.)
Assertion
Ref Expression
nesym  |-  ( A  =/=  B  <->  -.  B  =  A )

Proof of Theorem nesym
StepHypRef Expression
1 eqcom 2090 . 2  |-  ( A  =  B  <->  B  =  A )
21necon3abii 2291 1  |-  ( A  =/=  B  <->  -.  B  =  A )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103    = 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  ax-5 1381  ax-gen 1383  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-ne 2256
This theorem is referenced by:  nesymi  2301  nesymir  2302  0neqopab  5694  fzdifsuc  9495  isprm3  11378
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