Metamath Proof Explorer


Theorem bj-projex

Description: Sethood of the class projection. (Contributed by BJ, 6-Apr-2019)

Ref Expression
Assertion bj-projex ( 𝐵𝑉 → ( 𝐴 Proj 𝐵 ) ∈ V )

Proof

Step Hyp Ref Expression
1 df-bj-proj ( 𝐴 Proj 𝐵 ) = { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) }
2 bj-clex ( 𝐵𝑉 → { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) } ∈ V )
3 1 2 eqeltrid ( 𝐵𝑉 → ( 𝐴 Proj 𝐵 ) ∈ V )