Theorem exmidne 2968

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 2966	. 2 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵)
2	1	orri 875	1 ⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Syntax hints:   ∨ wo 860   = wceq 1570   ≠ wne 2958

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 210  df-or 861  df-ne 2959

This theorem is referenced by:  elnn1uz2  12950  hashv01gt1  14383  numclwwlk3lem2lem  30715  fconst7v  32946  hashxpe  33133  drngmxidlr  33741  constrfin  34117  constrelextdg2  34118  subfacp1lem6  35658  tendoeq2  41529  ax6e2ndeqVD  45600  ax6e2ndeqALT  45622