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Definition df-uss 22860
Description: Define the uniform structure extractor function. Similarly with df-topn 16688 this differs from df-unif 16579 when a structure has been restricted using df-ress 16482; 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 22857 . 2 class UnifSt
2 vf . . 3 setvar 𝑓
3 cvv 3469 . . 3 class V
42cv 1537 . . . . 5 class 𝑓
5 cunif 16566 . . . . 5 class UnifSet
64, 5cfv 6334 . . . 4 class (UnifSet‘𝑓)
7 cbs 16474 . . . . . 6 class Base
84, 7cfv 6334 . . . . 5 class (Base‘𝑓)
98, 8cxp 5530 . . . 4 class ((Base‘𝑓) × (Base‘𝑓))
10 crest 16685 . . . 4 class t
116, 9, 10co 7140 . . 3 class ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓)))
122, 3, 11cmpt 5122 . 2 class (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))
131, 12wceq 1538 1 wff UnifSt = (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))
Colors of variables: wff setvar class
This definition is referenced by:  ussval  22863
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