Theorem nnrecred

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 )

Proof

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 )