Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-ltpq Unicode version

Definition df-ltpq 9309
 Description: Define pre-ordering relation on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c 9519, and is intended to be used only by the construction. Similar to Definition 5 of [Suppes] p. 162. (Contributed by NM, 28-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
df-ltpq
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-ltpq
StepHypRef Expression
1 cltpq 9249 . 2
2 vx . . . . . . 7
32cv 1394 . . . . . 6
4 cnpi 9243 . . . . . . 7
54, 4cxp 5002 . . . . . 6
63, 5wcel 1818 . . . . 5
7 vy . . . . . . 7
87cv 1394 . . . . . 6
98, 5wcel 1818 . . . . 5
106, 9wa 369 . . . 4
11 c1st 6798 . . . . . . 7
123, 11cfv 5593 . . . . . 6
13 c2nd 6799 . . . . . . 7
148, 13cfv 5593 . . . . . 6
15 cmi 9245 . . . . . 6
1612, 14, 15co 6296 . . . . 5
178, 11cfv 5593 . . . . . 6
183, 13cfv 5593 . . . . . 6
1917, 18, 15co 6296 . . . . 5
20 clti 9246 . . . . 5
2116, 19, 20wbr 4452 . . . 4
2210, 21wa 369 . . 3
2322, 2, 7copab 4509 . 2
241, 23wceq 1395 1
 Colors of variables: wff setvar class This definition is referenced by:  ordpipq  9341  lterpq  9369
 Copyright terms: Public domain W3C validator