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	$$⊢\mathrm{lim\; sup}\left(F\right)\in {ℝ}^{*}$$

Proof

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