Theorem resdmss

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

	Ref	Expression
Assertion	resdmss	$$⊢\mathrm{dom}\left({A\upharpoonright }_B\right)\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		dmres	$$⊢\mathrm{dom}\left({A\upharpoonright }_B\right)=B\cap \mathrm{dom}A$$
2		inss1	$$⊢B\cap \mathrm{dom}A\subseteq B$$
3	1 2	eqsstri	$$⊢\mathrm{dom}\left({A\upharpoonright }_B\right)\subseteq B$$