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Definition df-en 7516
Description: Define the equinumerosity relation. Definition of [Enderton] p. 129. We define  ~~ to be a binary relation rather than a connective, so its arguments must be sets to be meaningful. This is acceptable because we do not consider equinumerosity for proper classes. We derive the usual definition as bren 7524. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
df-en  |-  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
Distinct variable group:    x, y, f

Detailed syntax breakdown of Definition df-en
StepHypRef Expression
1 cen 7512 . 2  class  ~~
2 vx . . . . . 6  setvar  x
32cv 1380 . . . . 5  class  x
4 vy . . . . . 6  setvar  y
54cv 1380 . . . . 5  class  y
6 vf . . . . . 6  setvar  f
76cv 1380 . . . . 5  class  f
83, 5, 7wf1o 5574 . . . 4  wff  f : x -1-1-onto-> y
98, 6wex 1597 . . 3  wff  E. f 
f : x -1-1-onto-> y
109, 2, 4copab 4491 . 2  class  { <. x ,  y >.  |  E. f  f : x -1-1-onto-> y }
111, 10wceq 1381 1  wff  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
Colors of variables: wff setvar class
This definition is referenced by:  relen  7520  bren  7524  enssdom  7539
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