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Definition df-uss 21973
Description: Define the uniform structure extractor function. Similarly with df-topn 16008 this differs from df-unif 15889 when a structure has been restricted using df-ress 15791; in this case the UnifSet component will still have a uniform set over the larger set, and this function fixes this by restricting the uniform set as well. (Contributed by Thierry Arnoux, 1-Dec-2017.)
Assertion
Ref Expression
df-uss UnifSt = (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))

Detailed syntax breakdown of Definition df-uss
StepHypRef Expression
1 cuss 21970 . 2 class UnifSt
2 vf . . 3 setvar 𝑓
3 cvv 3186 . . 3 class V
42cv 1479 . . . . 5 class 𝑓
5 cunif 15875 . . . . 5 class UnifSet
64, 5cfv 5849 . . . 4 class (UnifSet‘𝑓)
7 cbs 15784 . . . . . 6 class Base
84, 7cfv 5849 . . . . 5 class (Base‘𝑓)
98, 8cxp 5074 . . . 4 class ((Base‘𝑓) × (Base‘𝑓))
10 crest 16005 . . . 4 class t
116, 9, 10co 6607 . . 3 class ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓)))
122, 3, 11cmpt 4675 . 2 class (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))
131, 12wceq 1480 1 wff UnifSt = (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))
Colors of variables: wff setvar class
This definition is referenced by:  ussval  21976
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