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Definition df-en 7514
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 7522. (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 7510 . 2  class  ~~
2 vx . . . . . 6  setvar  x
32cv 1378 . . . . 5  class  x
4 vy . . . . . 6  setvar  y
54cv 1378 . . . . 5  class  y
6 vf . . . . . 6  setvar  f
76cv 1378 . . . . 5  class  f
83, 5, 7wf1o 5585 . . . 4  wff  f : x -1-1-onto-> y
98, 6wex 1596 . . 3  wff  E. f 
f : x -1-1-onto-> y
109, 2, 4copab 4504 . 2  class  { <. x ,  y >.  |  E. f  f : x -1-1-onto-> y }
111, 10wceq 1379 1  wff  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
Colors of variables: wff setvar class
This definition is referenced by:  relen  7518  bren  7522  enssdom  7537
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