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Metamath Proof Explorer

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	$⊢ (A = B \lor A \neq B)$

Step	Hyp	Ref	Expression
1		neqne	$⊢ \neg A = B \to A \neq B$
2	1	orri	$⊢ (A = B \lor A \neq B)$