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	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	rnexd	⊢ ( 𝜑 → ran 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		rnexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		rnexg	⊢ ( 𝐴 ∈ 𝑉 → ran 𝐴 ∈ V )
3	1 2	syl	⊢ ( 𝜑 → ran 𝐴 ∈ V )