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Metamath Proof Explorer

Theorem mpteq1d

Description: An equality theorem for the maps-to notation. (Contributed by Mario Carneiro, 11-Jun-2016)

		Ref	Expression
	Hypothesis	mpteq1d.1	$⊢ φ \to A = B$
	Assertion	mpteq1d	$⊢ φ \to (x \in A ⟼ C) = (x \in B ⟼ C)$

Step	Hyp	Ref	Expression
1		mpteq1d.1	$⊢ φ \to A = B$
2		mpteq1	$⊢ A = B \to (x \in A ⟼ C) = (x \in B ⟼ C)$
3	1 2	syl	$⊢ φ \to (x \in A ⟼ C) = (x \in B ⟼ C)$