Metamath Proof Explorer

Theorem uzid2

Description: Membership of the least member in an upper set of integers. (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Assertion uzid2 
|- ( M e. ( ZZ>= ` N ) -> M e. ( ZZ>= ` M ) )

Proof

Step Hyp Ref Expression
1 eluzelz 
 |-  ( M e. ( ZZ>= ` N ) -> M e. ZZ )
2 uzid 
 |-  ( M e. ZZ -> M e. ( ZZ>= ` M ) )
3 1 2 syl 
 |-  ( M e. ( ZZ>= ` N ) -> M e. ( ZZ>= ` M ) )