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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	⊢ ¬ 𝐴 ≠ 𝐴

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐴 = 𝐴
2		nne	⊢ ( ¬ 𝐴 ≠ 𝐴 ↔ 𝐴 = 𝐴 )
3	1 2	mpbir	⊢ ¬ 𝐴 ≠ 𝐴