Theorem imaex

Description: The image of a set is a set. Theorem 3.17 of Monk1 p. 39. (Contributed by JJ, 24-Sep-2021)

	Ref	Expression
Hypothesis	imaex.1	⊢ 𝐴 ∈ V
Assertion	imaex	⊢ ( 𝐴 “ 𝐵 ) ∈ V

Proof

Step	Hyp	Ref	Expression
1		imaex.1	⊢ 𝐴 ∈ V
2		imaexg	⊢ ( 𝐴 ∈ V → ( 𝐴 “ 𝐵 ) ∈ V )
3	1 2	ax-mp	⊢ ( 𝐴 “ 𝐵 ) ∈ V