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Metamath Proof Explorer

Theorem resmpti

Description: Restriction of the mapping operation. (Contributed by Glauco Siliprandi, 17-Aug-2020)

		Ref	Expression
	Hypothesis	resmpti.1	$⊢ B \subseteq A$
	Assertion	resmpti	$⊢ {(x \in A ⟼ C) ↾}_{B} = (x \in B ⟼ C)$

Step	Hyp	Ref	Expression
1		resmpti.1	$⊢ B \subseteq A$
2		resmpt	$⊢ B \subseteq A \to {(x \in A ⟼ C) ↾}_{B} = (x \in B ⟼ C)$
3	1 2	ax-mp	$⊢ {(x \in A ⟼ C) ↾}_{B} = (x \in B ⟼ C)$