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Definition df-dom 6833
Description: Define the dominance relation. For an alternate definition see dfdom2 6855. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 6842 and domen 6843. (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 6829 . 2  class  ~<_
2 vx . . . . . 6  set  x
32cv 1618 . . . . 5  class  x
4 vy . . . . . 6  set  y
54cv 1618 . . . . 5  class  y
6 vf . . . . . 6  set  f
76cv 1618 . . . . 5  class  f
83, 5, 7wf1 4670 . . . 4  wff  f : x -1-1-> y
98, 6wex 1537 . . 3  wff  E. f 
f : x -1-1-> y
109, 2, 4copab 4050 . 2  class  { <. x ,  y >.  |  E. f  f : x
-1-1-> y }
111, 10wceq 1619 1  wff  ~<_  =  { <. x ,  y >.  |  E. f  f : x -1-1-> y }
Colors of variables: wff set class
This definition is referenced by:  reldom  6837  brdomg  6840  enssdom  6854
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