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Metamath Proof Explorer

Theorem resdmss

Description: Subset relationship for the domain of a restriction. (Contributed by Scott Fenton, 9-Aug-2024)

		Ref	Expression
	Assertion	resdmss	$⊢ dom ({A ↾}_{B}) \subseteq B$

Step	Hyp	Ref	Expression
1		dmres	$⊢ dom ({A ↾}_{B}) = B \cap dom A$
2		inss1	$⊢ B \cap dom A \subseteq B$
3	1 2	eqsstri	$⊢ dom ({A ↾}_{B}) \subseteq B$