Theorem nnrecred

Description: The reciprocal of a positive integer is real. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	nnge1d.1	$$⊢\phi \to A\in \mathbb{N}$$
Assertion	nnrecred	$$⊢\phi \to \frac{1}{A}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		nnge1d.1	$$⊢\phi \to A\in \mathbb{N}$$
2		nnrecre	$$⊢A\in \mathbb{N}\to \frac{1}{A}\in ℝ$$
3	1 2	syl	$$⊢\phi \to \frac{1}{A}\in ℝ$$