Theorem liminfcld

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

	Ref	Expression
Hypothesis	liminfcld.1	|- ( ph -> F e. V )
Assertion	liminfcld	|- ( ph -> ( liminf ` F ) e. RR* )

Proof

Step	Hyp	Ref	Expression
1		liminfcld.1	|- ( ph -> F e. V )
2		liminfcl	|- ( F e. V -> ( liminf ` F ) e. RR* )
3	1 2	syl	|- ( ph -> ( liminf ` F ) e. RR* )