Theorem qdencl

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

	Ref	Expression
Assertion	qdencl	⊢ ( 𝐴 ∈ ℚ → ( denom ‘ 𝐴 ) ∈ ℕ )

Proof

Step	Hyp	Ref	Expression
1		qnumdencl	⊢ ( 𝐴 ∈ ℚ → ( ( numer ‘ 𝐴 ) ∈ ℤ ∧ ( denom ‘ 𝐴 ) ∈ ℕ ) )
2	1	simprd	⊢ ( 𝐴 ∈ ℚ → ( denom ‘ 𝐴 ) ∈ ℕ )