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Metamath Proof Explorer

Theorem ceicl

Description: The ceiling function returns an integer (closure law). (Contributed by Jeff Hankins, 10-Jun-2007)

		Ref	Expression
	Assertion	ceicl	$⊢ A \in ℝ \to - ⌊- A⌋ \in ℤ$

Step	Hyp	Ref	Expression
1		renegcl	$⊢ A \in ℝ \to - A \in ℝ$
2	1	flcld	$⊢ A \in ℝ \to ⌊- A⌋ \in ℤ$
3	2	znegcld	$⊢ A \in ℝ \to - ⌊- A⌋ \in ℤ$