This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem limsupcli

Description: Closure of the superior limit. (Contributed by Glauco Siliprandi, 2-Jan-2022)

		Ref	Expression
	Hypothesis	limsupcli.1	$⊢ F \in V$
	Assertion	limsupcli	$⊢ lim sup (F) \in ℝ^{*}$

Step	Hyp	Ref	Expression
1		limsupcli.1	$⊢ F \in V$
2		limsupcl	$⊢ F \in V \to lim sup (F) \in ℝ^{*}$
3	1 2	ax-mp	$⊢ lim sup (F) \in ℝ^{*}$