Theorem exmidne 2935

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 2933	. 2 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵)
2	1	orri 862	1 ⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Syntax hints:   ∨ wo 847   = wceq 1540   ≠ wne 2925

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 848  df-ne 2926

This theorem is referenced by:  elnn1uz2  12844  hashv01gt1  14270  numclwwlk3lem2lem  30345  hashxpe  32765  drngmxidlr  33428  constrfin  33715  constrelextdg2  33716  subfacp1lem6  35160  tendoeq2  40756  ax6e2ndeqVD  44885  ax6e2ndeqALT  44907