Theorem ceilcld

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

	Ref	Expression
Hypothesis	ceilcld.1	$$⊢\phi \to A\in ℝ$$
Assertion	ceilcld	$$⊢\phi \to ⌈A⌉\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		ceilcld.1	$$⊢\phi \to A\in ℝ$$
2		ceilcl	$$⊢A\in ℝ\to ⌈A⌉\in \mathbb{Z}$$
3	1 2	syl	$$⊢\phi \to ⌈A⌉\in \mathbb{Z}$$