Metamath Proof Explorer

Theorem uzssre

Description: An upper set of integers is a subset of the reals. (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Assertion uzssre 
|- ( ZZ>= ` M ) C_ RR

Proof

Step Hyp Ref Expression
1 uzssz 
 |-  ( ZZ>= ` M ) C_ ZZ
2 zssre 
 |-  ZZ C_ RR
3 1 2 sstri 
 |-  ( ZZ>= ` M ) C_ RR