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Definition df-wdom 7483
 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 8358), this concides with the 1-1 defition df-dom 7070; 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 7481 . 2 *
2 vx . . . . . 6
32cv 1648 . . . . 5
4 c0 3588 . . . . 5
53, 4wceq 1649 . . . 4
6 vy . . . . . . 7
76cv 1648 . . . . . 6
8 vz . . . . . . 7
98cv 1648 . . . . . 6
107, 3, 9wfo 5411 . . . . 5
1110, 8wex 1547 . . . 4
125, 11wo 358 . . 3
1312, 2, 6copab 4225 . 2
141, 13wceq 1649 1 *
 Colors of variables: wff set class This definition is referenced by:  relwdom  7490  brwdom  7491
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