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Mirrors > Home > ILE Home > Th. List > df-rp | GIF version |
Description: Define the set of positive reals. Definition of positive numbers in [Apostol] p. 20. (Contributed by NM, 27-Oct-2007.) |
Ref | Expression |
---|---|
df-rp | ⊢ ℝ+ = {𝑥 ∈ ℝ ∣ 0 < 𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crp 9610 | . 2 class ℝ+ | |
2 | cc0 7774 | . . . 4 class 0 | |
3 | vx | . . . . 5 setvar 𝑥 | |
4 | 3 | cv 1347 | . . . 4 class 𝑥 |
5 | clt 7954 | . . . 4 class < | |
6 | 2, 4, 5 | wbr 3989 | . . 3 wff 0 < 𝑥 |
7 | cr 7773 | . . 3 class ℝ | |
8 | 6, 3, 7 | crab 2452 | . 2 class {𝑥 ∈ ℝ ∣ 0 < 𝑥} |
9 | 1, 8 | wceq 1348 | 1 wff ℝ+ = {𝑥 ∈ ℝ ∣ 0 < 𝑥} |
Colors of variables: wff set class |
This definition is referenced by: elrp 9612 rpre 9617 ioorp 9908 |
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