Theorem uzred

Description: An upper integer is a real number. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypotheses	uzred.1	|- Z = ( ZZ>= ` M )
	uzred.2	|- ( ph -> A e. Z )
Assertion	uzred	|- ( ph -> A e. RR )

Proof

Step	Hyp	Ref	Expression
1		uzred.1	|- Z = ( ZZ>= ` M )
2		uzred.2	|- ( ph -> A e. Z )
3		zssre	|- ZZ C_ RR
4	1 2	eluzelz2d	|- ( ph -> A e. ZZ )
5	3 4	sseldi	|- ( ph -> A e. RR )