MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-lo1 Unicode version

Definition df-lo1 13314
Description: Define the set of eventually upper bounded real functions. This fills a gap in coverage, to express statements like f(x) (x) O(x) via (xe. |->(f(x) (x)) x)e. . (Contributed by Mario Carneiro, 25-May-2016.)
Assertion
Ref Expression
df-lo1
Distinct variable group:   , , ,

Detailed syntax breakdown of Definition df-lo1
StepHypRef Expression
1 clo1 13310 . 2
2 vy . . . . . . . . 9
32cv 1394 . . . . . . . 8
4 vf . . . . . . . . 9
54cv 1394 . . . . . . . 8
63, 5cfv 5593 . . . . . . 7
7 vm . . . . . . . 8
87cv 1394 . . . . . . 7
9 cle 9650 . . . . . . 7
106, 8, 9wbr 4452 . . . . . 6
115cdm 5004 . . . . . . 7
12 vx . . . . . . . . 9
1312cv 1394 . . . . . . . 8
14 cpnf 9646 . . . . . . . 8
15 cico 11560 . . . . . . . 8
1613, 14, 15co 6296 . . . . . . 7
1711, 16cin 3474 . . . . . 6
1810, 2, 17wral 2807 . . . . 5
19 cr 9512 . . . . 5
2018, 7, 19wrex 2808 . . . 4
2120, 12, 19wrex 2808 . . 3
22 cpm 7440 . . . 4
2319, 19, 22co 6296 . . 3
2421, 4, 23crab 2811 . 2
251, 24wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  ello1  13338
  Copyright terms: Public domain W3C validator