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Metamath Proof Explorer

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	$⊢ φ \to A \in ℝ$
	Assertion	ceilged	$⊢ φ \to A \leq ⌈A⌉$

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