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Theorem necomi 2340
Description: Inference from commutative law for inequality. (Contributed by NM, 17-Oct-2012.)
Hypothesis
Ref Expression
necomi.1 𝐴𝐵
Assertion
Ref Expression
necomi 𝐵𝐴

Proof of Theorem necomi
StepHypRef Expression
1 necomi.1 . 2 𝐴𝐵
2 necom 2339 . 2 (𝐴𝐵𝐵𝐴)
31, 2mpbi 143 1 𝐵𝐴
Colors of variables: wff set class
Syntax hints:  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:  0nep0  4000  xp01disj  6198  djulclb  6747  djuinr  6755  djuin  6756  pnfnemnf  7542  mnfnepnf  7543  ltneii  7581  1ne0  8490  0ne2  8621  fzprval  9496  0tonninf  9845  1tonninf  9846
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