Description: The reciprocal of a positive integer is rational. (Contributed by NM, 17-Nov-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | nnrecq | ⊢ ( 𝐴 ∈ ℕ → ( 1 / 𝐴 ) ∈ ℚ ) |
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 ) |