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

Definition df-ltxr 9654
Description: Define 'less than' on the set of extended reals. Definition 12-3.1 of [Gleason] p. 173. Note that in our postulates for complex numbers, is primitive and not necessarily a relation on . (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
df-ltxr
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-ltxr
StepHypRef Expression
1 clt 9649 . 2
2 vx . . . . . . 7
32cv 1394 . . . . . 6
4 cr 9512 . . . . . 6
53, 4wcel 1818 . . . . 5
6 vy . . . . . . 7
76cv 1394 . . . . . 6
87, 4wcel 1818 . . . . 5
9 cltrr 9517 . . . . . 6
103, 7, 9wbr 4452 . . . . 5
115, 8, 10w3a 973 . . . 4
1211, 2, 6copab 4509 . . 3
13 cmnf 9647 . . . . . . 7
1413csn 4029 . . . . . 6
154, 14cun 3473 . . . . 5
16 cpnf 9646 . . . . . 6
1716csn 4029 . . . . 5
1815, 17cxp 5002 . . . 4
1914, 4cxp 5002 . . . 4
2018, 19cun 3473 . . 3
2112, 20cun 3473 . 2
221, 21wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  ltrelxr  9669  ltxrlt  9676  ltxr  11353
  Copyright terms: Public domain W3C validator