ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  necomi GIF version

Theorem necomi 2334
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 2333 . 2 (𝐴𝐵𝐵𝐴)
31, 2mpbi 143 1 𝐵𝐴
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  6101  djuin  6556  pnfnemnf  7287  mnfnepnf  7288  ltneii  7326  1ne0  8226  0ne2  8356  fzprval  9227
  Copyright terms: Public domain W3C validator