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Theorem nesymir 2742
Description: Inference associated with nesym 2739. (Contributed by BJ, 7-Jul-2018.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Hypothesis
Ref Expression
nesymir.1  |-  -.  A  =  B
Assertion
Ref Expression
nesymir  |-  B  =/= 
A

Proof of Theorem nesymir
StepHypRef Expression
1 nesymir.1 . . 3  |-  -.  A  =  B
21neir 2667 . 2  |-  A  =/= 
B
32necomi 2737 1  |-  B  =/= 
A
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    = wceq 1379    =/= wne 2662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-cleq 2459  df-ne 2664
This theorem is referenced by: (None)
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