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 ∈ ℚ → ( numer ‘ 𝐴 ) ∈ ℤ )

Proof

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