Theorem nnrp

Description: A positive integer is a positive real. (Contributed by NM, 28-Nov-2008)

	Ref	Expression
Assertion	nnrp	$$⊢A\in \mathbb{N}\to A\in {ℝ}^{+}$$

Proof

Step	Hyp	Ref	Expression
1		nnre	$$⊢A\in \mathbb{N}\to A\in ℝ$$
2		nngt0	$$⊢A\in \mathbb{N}\to 0<A$$
3		elrp	$$⊢A\in {ℝ}^{+}\leftrightarrow \left(A\in ℝ\wedge 0<A\right)$$
4	1 2 3	sylanbrc	$$⊢A\in \mathbb{N}\to A\in {ℝ}^{+}$$