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

Theorem nesymi 2329
 Description: Inference associated with nesym 2328. (Contributed by BJ, 7-Jul-2018.)
Hypothesis
Ref Expression
nesymi.1 𝐴𝐵
Assertion
Ref Expression
nesymi ¬ 𝐵 = 𝐴

Proof of Theorem nesymi
StepHypRef Expression
1 nesymi.1 . 2 𝐴𝐵
2 nesym 2328 . 2 (𝐴𝐵 ↔ ¬ 𝐵 = 𝐴)
31, 2mpbi 144 1 ¬ 𝐵 = 𝐴
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   = wceq 1314   ≠ wne 2283 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 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2284 This theorem is referenced by:  frec0g  6260  djune  6929  omp1eomlem  6945  fodjum  6984  fodju0  6985  ismkvnex  6995  mkvprop  6998  xrltnr  9506  nltmnf  9514  xnn0xadd0  9590  pwle2  13004  nninfalllem1  13014  nninfall  13015  nninfsellemeq  13021
 Copyright terms: Public domain W3C validator