Metamath Proof Explorer


Theorem fdmexb

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 : 𝐴𝐵 → ( 𝐴 ∈ V ↔ 𝐹 ∈ V ) )

Proof

Step Hyp Ref Expression
1 ffn ( 𝐹 : 𝐴𝐵𝐹 Fn 𝐴 )
2 fndmexb ( 𝐹 Fn 𝐴 → ( 𝐴 ∈ V ↔ 𝐹 ∈ V ) )
3 1 2 syl ( 𝐹 : 𝐴𝐵 → ( 𝐴 ∈ V ↔ 𝐹 ∈ V ) )