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	$$⊢\left(A=B\vee A\ne B\right)$$

Proof

Step	Hyp	Ref	Expression
1		neqne	$$⊢\neg A=B\to A\ne B$$
2	1	orri	$$⊢\left(A=B\vee A\ne B\right)$$