Theorem supxrcli

Description: The supremum of an arbitrary set of extended reals is an extended real. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	supxrcli.1	|- A C_ RR*
Assertion	supxrcli	|- sup ( A , RR* , < ) e. RR*

Proof

Step	Hyp	Ref	Expression
1		supxrcli.1	|- A C_ RR*
2		supxrcl	|- ( A C_ RR* -> sup ( A , RR* , < ) e. RR* )
3	1 2	ax-mp	|- sup ( A , RR* , < ) e. RR*