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 ) |
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 ) |