Theorem rnresss

Description: The range of a restriction is a subset of the whole range. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Assertion	rnresss	$$⊢\mathrm{ran}\left({A\upharpoonright }_B\right)\subseteq \mathrm{ran}A$$

Proof

Step	Hyp	Ref	Expression
1		resss	$$⊢{A\upharpoonright }_B\subseteq A$$
2	1	rnssi	$$⊢\mathrm{ran}\left({A\upharpoonright }_B\right)\subseteq \mathrm{ran}A$$