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Metamath Proof Explorer

Theorem flcld

Description: The floor (greatest integer) function is an integer (closure law). (Contributed by Mario Carneiro, 28-May-2016)

		Ref	Expression
	Hypothesis	flcld.1	$⊢ φ \to A \in ℝ$
	Assertion	flcld	$⊢ φ \to ⌊A⌋ \in ℤ$

Step	Hyp	Ref	Expression
1		flcld.1	$⊢ φ \to A \in ℝ$
2		flcl	$⊢ A \in ℝ \to ⌊A⌋ \in ℤ$
3	1 2	syl	$⊢ φ \to ⌊A⌋ \in ℤ$