Theorem elfvex

Description: If a function value has a member, then the argument is a set. (An artifact of our function value definition.) (Contributed by Mario Carneiro, 6-Nov-2015)

	Ref	Expression
Assertion	elfvex	⊢ ( 𝐴 ∈ ( 𝐹 ‘ 𝐵 ) → 𝐵 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		elfvdm	⊢ ( 𝐴 ∈ ( 𝐹 ‘ 𝐵 ) → 𝐵 ∈ dom 𝐹 )
2	1	elexd	⊢ ( 𝐴 ∈ ( 𝐹 ‘ 𝐵 ) → 𝐵 ∈ V )