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Metamath Proof Explorer

Theorem nnrecre

Description: The reciprocal of a positive integer is real. (Contributed by NM, 8-Feb-2008)

		Ref	Expression
	Assertion	nnrecre	$⊢ N \in ℕ \to \frac{1}{N} \in ℝ$

Step	Hyp	Ref	Expression
1		1re	$⊢ 1 \in ℝ$
2		nndivre	$⊢ (1 \in ℝ \land N \in ℕ) \to \frac{1}{N} \in ℝ$
3	1 2	mpan	$⊢ N \in ℕ \to \frac{1}{N} \in ℝ$