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Theorem necomi 2334
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 2333 . 2  |-  ( A  =/=  B  <->  B  =/=  A )
31, 2mpbi 143 1  |-  B  =/= 
A
Colors of variables: wff set class
Syntax hints:    =/= wne 2249
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 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by:  0nep0  3959  xp01disj  6102  djuin  6562  pnfnemnf  7305  mnfnepnf  7306  ltneii  7344  1ne0  8244  0ne2  8374  fzprval  9245
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