Theorem limsupcld

Description: Closure of the superior limit. (Contributed by Glauco Siliprandi, 23-Oct-2021)

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

Proof

Step	Hyp	Ref	Expression
1		limsupcld.1	|- ( ph -> F e. V )
2		limsupcl	|- ( F e. V -> ( limsup ` F ) e. RR* )
3	1 2	syl	|- ( ph -> ( limsup ` F ) e. RR* )