Theorem rnexd

Description: The range of a set is a set. Deduction version of rnexd . (Contributed by Thierry Arnoux, 14-Feb-2025)

	Ref	Expression
Hypothesis	rnexd.1	$$⊢\phi \to A\in V$$
Assertion	rnexd	$$⊢\phi \to \mathrm{ran}A\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		rnexd.1	$$⊢\phi \to A\in V$$
2		rnexg	$$⊢A\in V\to \mathrm{ran}A\in \mathrm{V}$$
3	1 2	syl	$$⊢\phi \to \mathrm{ran}A\in \mathrm{V}$$