Theorem ioorp

Description: The set of positive reals expressed as an open interval. (Contributed by Steve Rodriguez, 25-Nov-2007)

	Ref	Expression
Assertion	ioorp	⊢ ( 0 (,) +∞ ) = ℝ+

Proof

Step	Hyp	Ref	Expression
1		ioopos	⊢ ( 0 (,) +∞ ) = { 𝑥 ∈ ℝ ∣ 0 < 𝑥 }
2		df-rp	⊢ ℝ+ = { 𝑥 ∈ ℝ ∣ 0 < 𝑥 }
3	1 2	eqtr4i	⊢ ( 0 (,) +∞ ) = ℝ+