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Definition df-ltp 9767
Description: Define ordering on positive reals. This is a "temporary" set used in the construction of complex numbers df-c 9902, and is intended to be used only by the construction. From Proposition 9-3.2 of [Gleason] p. 122. (Contributed by NM, 14-Feb-1996.) (New usage is discouraged.)
Assertion
Ref Expression
df-ltp <P = {⟨𝑥, 𝑦⟩ ∣ ((𝑥P𝑦P) ∧ 𝑥𝑦)}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-ltp
StepHypRef Expression
1 cltp 9645 . 2 class <P
2 vx . . . . . . 7 setvar 𝑥
32cv 1479 . . . . . 6 class 𝑥
4 cnp 9641 . . . . . 6 class P
53, 4wcel 1987 . . . . 5 wff 𝑥P
6 vy . . . . . . 7 setvar 𝑦
76cv 1479 . . . . . 6 class 𝑦
87, 4wcel 1987 . . . . 5 wff 𝑦P
95, 8wa 384 . . . 4 wff (𝑥P𝑦P)
103, 7wpss 3561 . . . 4 wff 𝑥𝑦
119, 10wa 384 . . 3 wff ((𝑥P𝑦P) ∧ 𝑥𝑦)
1211, 2, 6copab 4682 . 2 class {⟨𝑥, 𝑦⟩ ∣ ((𝑥P𝑦P) ∧ 𝑥𝑦)}
131, 12wceq 1480 1 wff <P = {⟨𝑥, 𝑦⟩ ∣ ((𝑥P𝑦P) ∧ 𝑥𝑦)}
Colors of variables: wff setvar class
This definition is referenced by:  ltrelpr  9780  ltprord  9812
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