This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem neirr

Description: No class is unequal to itself. Inequality is irreflexive. (Contributed by Stefan O'Rear, 1-Jan-2015)

		Ref	Expression
	Assertion	neirr	$⊢ \neg A \neq A$

Step	Hyp	Ref	Expression
1		eqid	$⊢ A = A$
2		nne	$⊢ \neg A \neq A \leftrightarrow A = A$
3	1 2	mpbir	$⊢ \neg A \neq A$