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Definition df-en 6719
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 6725. (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 6716 . 2  class  ~~
2 vx . . . . . 6  setvar  x
32cv 1347 . . . . 5  class  x
4 vy . . . . . 6  setvar  y
54cv 1347 . . . . 5  class  y
6 vf . . . . . 6  setvar  f
76cv 1347 . . . . 5  class  f
83, 5, 7wf1o 5197 . . . 4  wff  f : x -1-1-onto-> y
98, 6wex 1485 . . 3  wff  E. f 
f : x -1-1-onto-> y
109, 2, 4copab 4049 . 2  class  { <. x ,  y >.  |  E. f  f : x -1-1-onto-> y }
111, 10wceq 1348 1  wff  ~~  =  { <. x ,  y
>.  |  E. f 
f : x -1-1-onto-> y }
Colors of variables: wff set class
This definition is referenced by:  relen  6722  bren  6725  enssdom  6740
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