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Theorem necomi 2391
Description: Inference from commutative law for inequality. (Contributed by NM, 17-Oct-2012.)
Hypothesis
Ref Expression
necomi.1  |-  A  =/= 
B
Assertion
Ref Expression
necomi  |-  B  =/= 
A

Proof of Theorem necomi
StepHypRef Expression
1 necomi.1 . 2  |-  A  =/= 
B
2 necom 2390 . 2  |-  ( A  =/=  B  <->  B  =/=  A )
31, 2mpbi 144 1  |-  B  =/= 
A
Colors of variables: wff set class
Syntax hints:    =/= wne 2306
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 2119
This theorem depends on definitions:  df-bi 116  df-cleq 2130  df-ne 2307
This theorem is referenced by:  0nep0  4084  xp01disj  6323  xp01disjl  6324  djulclb  6933  djuinr  6941  pnfnemnf  7813  mnfnepnf  7814  ltneii  7853  1ne0  8781  0ne2  8918  fzprval  9855  0tonninf  10205  1tonninf  10206
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