Metamath Proof Explorer

Theorem ceilcld

Description: Closure of the ceiling function. (Contributed by Glauco Siliprandi, 2-Jan-2022)

Ref Expression
Hypothesis ceilcld.1 
|- ( ph -> A e. RR )
Assertion ceilcld 
|- ( ph -> ( |^ ` A ) e. ZZ )

Proof

Step Hyp Ref Expression
1 ceilcld.1 
 |-  ( ph -> A e. RR )
2 ceilcl 
 |-  ( A e. RR -> ( |^ ` A ) e. ZZ )
3 1 2 syl 
 |-  ( ph -> ( |^ ` A ) e. ZZ )