Theorem exmidne 2947

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 2945	. 2 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵)
2	1	orri 862	1 ⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Syntax hints:   ∨ wo 847   = wceq 1536   ≠ wne 2937

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 2938

This theorem is referenced by:  elnn1uz2  12964  hashv01gt1  14380  numclwwlk3lem2lem  30411  hashxpe  32816  drngmxidlr  33485  constrfin  33750  constrelextdg2  33751  subfacp1lem6  35169  tendoeq2  40756  ax6e2ndeqVD  44906  ax6e2ndeqALT  44928