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Metamath Proof Explorer

Theorem sneqd

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

		Ref	Expression
	Hypothesis	sneqd.1	$⊢ φ \to A = B$
	Assertion	sneqd	$⊢ φ \to \{A\} = \{B\}$

Step	Hyp	Ref	Expression
1		sneqd.1	$⊢ φ \to A = B$
2		sneq	$⊢ A = B \to \{A\} = \{B\}$
3	1 2	syl	$⊢ φ \to \{A\} = \{B\}$