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Definition df-ge 25248
Description: Define the greatest element of a poset. I.e. the element of the poset that is larger than the other elements. Meaningful is  r is at least a poset (otherwise there could be more than one supremum due to cycles). Bourbaki E III 10. Experimental. (Contributed by FL, 19-Sep-2011.)
Assertion
Ref Expression
df-ge  |-  ge  =  ( r  e.  _V  |->  ( r  sup w  dom  r ) )

Detailed syntax breakdown of Definition df-ge
StepHypRef Expression
1 cge 25220 . 2  class  ge
2 vr . . 3  set  r
3 cvv 2788 . . 3  class  _V
42cv 1622 . . . 4  class  r
54cdm 4689 . . . 4  class  dom  r
6 cspw 14303 . . . 4  class  sup w
74, 5, 6co 5858 . . 3  class  ( r  sup w  dom  r
)
82, 3, 7cmpt 4077 . 2  class  ( r  e.  _V  |->  ( r  sup w  dom  r
) )
91, 8wceq 1623 1  wff  ge  =  ( r  e.  _V  |->  ( r  sup w  dom  r ) )
Colors of variables: wff set class
This definition is referenced by:  gepsup  25250
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