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Definition df-dom 6861
Description: Define the dominance relation. For an alternate definition see dfdom2 6883. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 6870 and domen 6871. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
df-dom  |-  ~<_  =  { <. x ,  y >.  |  E. f  f : x -1-1-> y }
Distinct variable group:    x, y, f

Detailed syntax breakdown of Definition df-dom
StepHypRef Expression
1 cdom 6857 . 2  class  ~<_
2 vx . . . . . 6  set  x
32cv 1623 . . . . 5  class  x
4 vy . . . . . 6  set  y
54cv 1623 . . . . 5  class  y
6 vf . . . . . 6  set  f
76cv 1623 . . . . 5  class  f
83, 5, 7wf1 5219 . . . 4  wff  f : x -1-1-> y
98, 6wex 1529 . . 3  wff  E. f 
f : x -1-1-> y
109, 2, 4copab 4078 . 2  class  { <. x ,  y >.  |  E. f  f : x
-1-1-> y }
111, 10wceq 1624 1  wff  ~<_  =  { <. x ,  y >.  |  E. f  f : x -1-1-> y }
Colors of variables: wff set class
This definition is referenced by:  reldom  6865  brdomg  6868  enssdom  6882
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