Theorem ceilged

Description: The ceiling of a real number is greater than or equal to that number. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	ceilged.1	$$⊢\phi \to A\in ℝ$$
Assertion	ceilged	$$⊢\phi \to A\le ⌈A⌉$$

Proof

Step	Hyp	Ref	Expression
1		ceilged.1	$$⊢\phi \to A\in ℝ$$
2		ceilge	$$⊢A\in ℝ\to A\le ⌈A⌉$$
3	1 2	syl	$$⊢\phi \to A\le ⌈A⌉$$