Theorem nnrp

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

	Ref	Expression
Assertion	nnrp	⊢ ( 𝐴 ∈ ℕ → 𝐴 ∈ ℝ+ )

Proof

Step	Hyp	Ref	Expression
1		nnre	⊢ ( 𝐴 ∈ ℕ → 𝐴 ∈ ℝ )
2		nngt0	⊢ ( 𝐴 ∈ ℕ → 0 < 𝐴 )
3		elrp	⊢ ( 𝐴 ∈ ℝ+ ↔ ( 𝐴 ∈ ℝ ∧ 0 < 𝐴 ) )
4	1 2 3	sylanbrc	⊢ ( 𝐴 ∈ ℕ → 𝐴 ∈ ℝ+ )