Users' Mathboxes Mathbox for David A. Wheeler < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-gt Structured version   Visualization version   GIF version

Definition df-gt 51094
Description: The 'greater than' relation is merely the converse of the 'less than or equal to' relation defined by df-lt 11237. Defined in ISO 80000-2:2009(E) operation 2-7.12. See df-gte 51093 for a discussion on why this approach is used for the definition. See gt-lt 51096 and gt-lth 51098 for more conventional expression of the relationship between < and >.

As a stylistic issue, set.mm prefers 'less than or equal' instead of 'greater than or equal' to reduce the number of conversion steps. Thus, we discourage its use, but include its definition so that there is a formal definition of this symbol.

(Contributed by David A. Wheeler, 19-Apr-2015.) (New usage is discouraged.)

Assertion
Ref Expression
df-gt > = ◡ <

Detailed syntax breakdown of Definition df-gt
StepHypRef Expression
1 cgt 51092 . 2 class >
2 clt 11367 . . 3 class <
32ccnv 5654 . 2 class ◡ <
41, 3wceq 1570 1 wff > = ◡ <
Colors of variables:    wff setvar class
This definition is used by:  gt-lt  51096  gt-lth  51098
  Copyright terms: Public domain W3C validator