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Metamath Proof Explorer

Definition df-rp

Description: Define the set of positive reals. Definition of positive numbers in Apostol p. 20. (Contributed by NM, 27-Oct-2007)

		Ref	Expression
	Assertion	df-rp	$⊢ ℝ^{+} = \{x \in ℝ \| 0 < x\}$

Step	Hyp	Ref	Expression
0		crp	$class ℝ^{+}$
1		vx	$setvar x$
2		cr	$class ℝ$
3		cc0	$class 0$
4		clt	$class <$
5	1	cv	$setvar x$
6	3 5 4	wbr	$wff 0 < x$
7	6 1 2	crab	$class \{x \in ℝ \| 0 < x\}$
8	0 7	wceq	$wff ℝ^{+} = \{x \in ℝ \| 0 < x\}$