Metamath Proof Explorer


Theorem ulmscl

Description: Closure of the base set in a uniform limit. (Contributed by Mario Carneiro, 26-Feb-2015)

Ref Expression
Assertion ulmscl ( 𝐹 ( ⇝𝑢𝑆 ) 𝐺𝑆 ∈ V )

Proof

Step Hyp Ref Expression
1 df-br ( 𝐹 ( ⇝𝑢𝑆 ) 𝐺 ↔ ⟨ 𝐹 , 𝐺 ⟩ ∈ ( ⇝𝑢𝑆 ) )
2 elfvex ( ⟨ 𝐹 , 𝐺 ⟩ ∈ ( ⇝𝑢𝑆 ) → 𝑆 ∈ V )
3 1 2 sylbi ( 𝐹 ( ⇝𝑢𝑆 ) 𝐺𝑆 ∈ V )