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Metamath Proof Explorer

Theorem qdencl

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

		Ref	Expression
	Assertion	qdencl	$⊢ A \in ℚ \to denom (A) \in ℕ$

Step	Hyp	Ref	Expression
1		qnumdencl	$⊢ A \in ℚ \to (numer (A) \in ℤ \land denom (A) \in ℕ)$
2	1	simprd	$⊢ A \in ℚ \to denom (A) \in ℕ$