Theorem exmidne 2966

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 2964	. 2 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵)
2	1	orri 873	1 ⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Syntax hints:   ∨ wo 858   = wceq 1559   ≠ wne 2956

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 209  df-or 859  df-ne 2957

This theorem is referenced by:  elnn1uz2  12920  hashv01gt1  14352  numclwwlk3lem2lem  30542  fconst7v  32783  hashxpe  32970  drngmxidlr  33627  constrfin  34004  constrelextdg2  34005  subfacp1lem6  35496  tendoeq2  41359  ax6e2ndeqVD  45445  ax6e2ndeqALT  45467