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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	$⊢ F \underset{u}{⇝} (S) G \to S \in V$

Step	Hyp	Ref	Expression
1		df-br	$⊢ F \underset{u}{⇝} (S) G \leftrightarrow ⟨F, G⟩ \in \underset{u}{⇝} (S)$
2		elfvex	$⊢ ⟨F, G⟩ \in \underset{u}{⇝} (S) \to S \in V$
3	1 2	sylbi	$⊢ F \underset{u}{⇝} (S) G \to S \in V$