Description: The reciprocal of a positive integer is real. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | nnge1d.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℕ ) | |
Assertion | nnrecred | ⊢ ( 𝜑 → ( 1 / 𝐴 ) ∈ ℝ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnge1d.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℕ ) | |
2 | nnrecre | ⊢ ( 𝐴 ∈ ℕ → ( 1 / 𝐴 ) ∈ ℝ ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 1 / 𝐴 ) ∈ ℝ ) |