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Metamath Proof Explorer

Theorem qnumcl

Description: The canonical numerator of a rational is an integer. (Contributed by Stefan O'Rear, 13-Sep-2014)

		Ref	Expression
	Assertion	qnumcl	$⊢ A \in ℚ \to numer (A) \in ℤ$

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