Theorem exmidne 2943

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 2941	. 2 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵)
2	1	orri 863	1 ⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Syntax hints:   ∨ wo 848   = wceq 1542   ≠ wne 2933

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 207  df-or 849  df-ne 2934

This theorem is referenced by:  elnn1uz2  12850  hashv01gt1  14280  numclwwlk3lem2lem  30470  fconst7v  32709  hashxpe  32897  drngmxidlr  33570  constrfin  33923  constrelextdg2  33924  subfacp1lem6  35398  tendoeq2  41147  ax6e2ndeqVD  45261  ax6e2ndeqALT  45283