Theorem nnrecq

Description: The reciprocal of a positive integer is rational. (Contributed by NM, 17-Nov-2004)

	Ref	Expression
Assertion	nnrecq	⊢ ( 𝐴 ∈ ℕ → ( 1 / 𝐴 ) ∈ ℚ )

Proof

Step	Hyp	Ref	Expression
1		1z	⊢ 1 ∈ ℤ
2		znq	⊢ ( ( 1 ∈ ℤ ∧ 𝐴 ∈ ℕ ) → ( 1 / 𝐴 ) ∈ ℚ )
3	1 2	mpan	⊢ ( 𝐴 ∈ ℕ → ( 1 / 𝐴 ) ∈ ℚ )