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Definition df-wdom 8006
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 8923), this coincides with the 1-1 definition df-dom 7538; 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
Distinct variable group:   , ,

Detailed syntax breakdown of Definition df-wdom
StepHypRef Expression
1 cwdom 8004 . 2
2 vx . . . . . 6
32cv 1394 . . . . 5
4 c0 3784 . . . . 5
53, 4wceq 1395 . . . 4
6 vy . . . . . . 7
76cv 1394 . . . . . 6
8 vz . . . . . . 7
98cv 1394 . . . . . 6
107, 3, 9wfo 5591 . . . . 5
1110, 8wex 1612 . . . 4
125, 11wo 368 . . 3
1312, 2, 6copab 4509 . 2
141, 13wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  relwdom  8013  brwdom  8014
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