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Theorem neir 2654
Description: Inference associated with df-ne 2651. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
neir.1  |-  -.  A  =  B
Assertion
Ref Expression
neir  |-  A  =/= 
B

Proof of Theorem neir
StepHypRef Expression
1 neir.1 . 2  |-  -.  A  =  B
2 df-ne 2651 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
31, 2mpbir 209 1  |-  A  =/= 
B
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    = wceq 1398    =/= wne 2649
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-ne 2651
This theorem is referenced by:  nesymir  2729  nsuceq0  4947  ax1ne0  9526  ine0  9988  nnunb  10787  nosgnn0i  29659  bj-pinftynminfty  35030
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