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Metamath Proof Explorer

Theorem nnrecred

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

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

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