Metamath Proof Explorer


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 )