Theorem ioorp

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

	Ref	Expression
Assertion	ioorp	$$⊢\left(0,\mathrm{+\infty }\right)={ℝ}^{+}$$

Proof

Step	Hyp	Ref	Expression
1		ioopos	$$⊢\left(0,\mathrm{+\infty }\right)=\left\{x\in ℝ|0<x\right\}$$
2		df-rp	$$⊢{ℝ}^{+}=\left\{x\in ℝ|0<x\right\}$$
3	1 2	eqtr4i	$$⊢\left(0,\mathrm{+\infty }\right)={ℝ}^{+}$$