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 (,) +oo ) = RR+

Proof

Step	Hyp	Ref	Expression
1		ioopos	|- ( 0 (,) +oo ) = { x e. RR | 0 < x }
2		df-rp	|- RR+ = { x e. RR | 0 < x }
3	1 2	eqtr4i	|- ( 0 (,) +oo ) = RR+