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Definition df-wdom 7779
Description: A set is weakly dominated by a "larger" set iff the "larger" set can be mapped onto the "smaller" set or the smaller set is empty; equivalently if the smaller set can be placed into bijection with some partition of the larger set. When choice is assumed (as fodom 8696), this coincides with the 1-1 definition df-dom 7317; however, it is not known whether this is a choice-equivalent or a strictly weaker form. Some discussion of this question can be found at http://boolesrings.org/asafk/2014/on-the-partition-principle/. (Contributed by Stefan O'Rear, 11-Feb-2015.)
Assertion
Ref Expression
df-wdom  |-  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
Distinct variable group:    x, y, z

Detailed syntax breakdown of Definition df-wdom
StepHypRef Expression
1 cwdom 7777 . 2  class  ~<_*
2 vx . . . . . 6  setvar  x
32cv 1368 . . . . 5  class  x
4 c0 3642 . . . . 5  class  (/)
53, 4wceq 1369 . . . 4  wff  x  =  (/)
6 vy . . . . . . 7  setvar  y
76cv 1368 . . . . . 6  class  y
8 vz . . . . . . 7  setvar  z
98cv 1368 . . . . . 6  class  z
107, 3, 9wfo 5421 . . . . 5  wff  z : y -onto-> x
1110, 8wex 1586 . . . 4  wff  E. z 
z : y -onto-> x
125, 11wo 368 . . 3  wff  ( x  =  (/)  \/  E. z 
z : y -onto-> x )
1312, 2, 6copab 4354 . 2  class  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
141, 13wceq 1369 1  wff  ~<_*  =  { <. x ,  y >.  |  ( x  =  (/)  \/  E. z  z : y
-onto-> x ) }
Colors of variables: wff setvar class
This definition is referenced by:  relwdom  7786  brwdom  7787
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