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Metamath Proof Explorer

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 sselid 
 |-  ( ph -> A e. RR )