Theorem qdencl

Description: The canonical denominator is a positive integer. (Contributed by Stefan O'Rear, 13-Sep-2014)

	Ref	Expression
Assertion	qdencl	$$⊢A\in \mathbb{Q}\to \mathrm{denom}\left(A\right)\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		qnumdencl	$$⊢A\in \mathbb{Q}\to \left(\mathrm{numer}\left(A\right)\in \mathbb{Z}\wedge \mathrm{denom}\left(A\right)\in \mathbb{N}\right)$$
2	1	simprd	$$⊢A\in \mathbb{Q}\to \mathrm{denom}\left(A\right)\in \mathbb{N}$$