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Definition df-uss 22580
 Description: Define the uniform structure extractor function. Similarly with df-topn 16551 this differs from df-unif 16442 when a structure has been restricted using df-ress 16345; 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 22577 . 2 class UnifSt
2 vf . . 3 setvar 𝑓
3 cvv 3409 . . 3 class V
42cv 1506 . . . . 5 class 𝑓
5 cunif 16429 . . . . 5 class UnifSet
64, 5cfv 6185 . . . 4 class (UnifSet‘𝑓)
7 cbs 16337 . . . . . 6 class Base
84, 7cfv 6185 . . . . 5 class (Base‘𝑓)
98, 8cxp 5401 . . . 4 class ((Base‘𝑓) × (Base‘𝑓))
10 crest 16548 . . . 4 class t
116, 9, 10co 6974 . . 3 class ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓)))
122, 3, 11cmpt 5004 . 2 class (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))
131, 12wceq 1507 1 wff UnifSt = (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))
 Colors of variables: wff setvar class This definition is referenced by:  ussval  22583
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