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Metamath Proof Explorer

Theorem sneqi

Description: Equality inference for singletons. (Contributed by NM, 22-Jan-2004)

		Ref	Expression
	Hypothesis	sneqi.1	$⊢ A = B$
	Assertion	sneqi	$⊢ \{A\} = \{B\}$

Step	Hyp	Ref	Expression
1		sneqi.1	$⊢ A = B$
2		sneq	$⊢ A = B \to \{A\} = \{B\}$
3	1 2	ax-mp	$⊢ \{A\} = \{B\}$