Theorem liminfcld

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

	Ref	Expression
Hypothesis	liminfcld.1	$$⊢\phi \to F\in V$$
Assertion	liminfcld	$$⊢\phi \to \mathrm{lim\; inf}\left(F\right)\in {ℝ}^{*}$$

Proof

Step	Hyp	Ref	Expression
1		liminfcld.1	$$⊢\phi \to F\in V$$
2		liminfcl	$$⊢F\in V\to \mathrm{lim\; inf}\left(F\right)\in {ℝ}^{*}$$
3	1 2	syl	$$⊢\phi \to \mathrm{lim\; inf}\left(F\right)\in {ℝ}^{*}$$