Theorem exmidne 2977

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 2975	. 2 ⊢ (¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵)
2	1	orri 848	1 ⊢ (𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵)

Syntax hints:   ∨ wo 833   = wceq 1507   ≠ wne 2967

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 199  df-or 834  df-ne 2968

This theorem is referenced by:  elnn1uz2  12142  hashv01gt1  13523  numclwwlk3lem2lem  27943  hashxpe  30279  subfacp1lem6  32017  tendoeq2  37355  ax6e2ndeqVD  40662  ax6e2ndeqALT  40684