Description: The domain of a function is a set iff the function is a set. (Contributed by AV, 8-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | fdmexb | ⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ( 𝐴 ∈ V ↔ 𝐹 ∈ V ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn | ⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 Fn 𝐴 ) | |
2 | fndmexb | ⊢ ( 𝐹 Fn 𝐴 → ( 𝐴 ∈ V ↔ 𝐹 ∈ V ) ) | |
3 | 1 2 | syl | ⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ( 𝐴 ∈ V ↔ 𝐹 ∈ V ) ) |