Theorem exmidne

Description: Excluded middle with equality and inequality. (Contributed by NM, 3-Feb-2012) (Proof shortened by Wolf Lammen, 17-Nov-2019)

	Ref	Expression
Assertion	exmidne	⊢ ( 𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		neqne	⊢ ( ¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵 )
2	1	orri	⊢ ( 𝐴 = 𝐵 ∨ 𝐴 ≠ 𝐵 )