Theorem bj-clex

Description: Sethood of certain classes. (Contributed by BJ, 2-Apr-2019)

	Ref	Expression
Assertion	bj-clex	⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∣ { 𝑥 } ∈ ( 𝐴 “ 𝐵 ) } ∈ V )

Proof

Step	Hyp	Ref	Expression
1		imaexg	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 “ 𝐵 ) ∈ V )
2		bj-snsetex	⊢ ( ( 𝐴 “ 𝐵 ) ∈ V → { 𝑥 ∣ { 𝑥 } ∈ ( 𝐴 “ 𝐵 ) } ∈ V )
3	1 2	syl	⊢ ( 𝐴 ∈ 𝑉 → { 𝑥 ∣ { 𝑥 } ∈ ( 𝐴 “ 𝐵 ) } ∈ V )