Description: Sethood of the class projection. (Contributed by BJ, 6-Apr-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | bj-projex | ⊢ ( 𝐵 ∈ 𝑉 → ( 𝐴 Proj 𝐵 ) ∈ V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-bj-proj | ⊢ ( 𝐴 Proj 𝐵 ) = { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) } | |
2 | bj-clex | ⊢ ( 𝐵 ∈ 𝑉 → { 𝑥 ∣ { 𝑥 } ∈ ( 𝐵 “ { 𝐴 } ) } ∈ V ) | |
3 | 1 2 | eqeltrid | ⊢ ( 𝐵 ∈ 𝑉 → ( 𝐴 Proj 𝐵 ) ∈ V ) |