Theorem rnssi

Description: Subclass inference for range. (Contributed by Peter Mazsa, 24-Sep-2022)

	Ref	Expression
Hypothesis	rnssi.1	$$⊢A\subseteq B$$
Assertion	rnssi	$$⊢\mathrm{ran}A\subseteq \mathrm{ran}B$$

Proof

Step	Hyp	Ref	Expression
1		rnssi.1	$$⊢A\subseteq B$$
2		rnss	$$⊢A\subseteq B\to \mathrm{ran}A\subseteq \mathrm{ran}B$$
3	1 2	ax-mp	$$⊢\mathrm{ran}A\subseteq \mathrm{ran}B$$