Theorem exmidne 2944

Description: Excluded middle with equality and inequality. (Contributed by NM, 3-Feb-2012.) (Proof shortened by Wolf Lammen, 17-Nov-2019.)

Assertion

Ref	Expression
exmidne	⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Proof of Theorem exmidne

Step	Hyp	Ref	Expression
1		neqne 2942	. 2 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵)
2	1	orri 868	1 ⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Syntax hints:   ∨ wo 853   = wceq 1547   ≠ wne 2934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 208  df-or 854  df-ne 2935

This theorem is referenced by:  elnn1uz2  12866  hashv01gt1  14298  numclwwlk3lem2lem  30471  fconst7v  32712  hashxpe  32899  drngmxidlr  33561  constrfin  33930  constrelextdg2  33931  subfacp1lem6  35413  tendoeq2  41266  ax6e2ndeqVD  45352  ax6e2ndeqALT  45374