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

Step	Hyp	Ref	Expression
1		cuss 22577	. 2 class UnifSt
2		vf	. . 3 setvar 𝑓
3		cvv 3409	. . 3 class V
4	2	cv 1506	. . . . 5 class 𝑓
5		cunif 16429	. . . . 5 class UnifSet
6	4, 5	cfv 6185	. . . 4 class (UnifSet‘𝑓)
7		cbs 16337	. . . . . 6 class Base
8	4, 7	cfv 6185	. . . . 5 class (Base‘𝑓)
9	8, 8	cxp 5401	. . . 4 class ((Base‘𝑓) × (Base‘𝑓))
10		crest 16548	. . . 4 class ↾t
11	6, 9, 10	co 6974	. . 3 class ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓)))
12	2, 3, 11	cmpt 5004	. 2 class (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))
13	1, 12	wceq 1507	1 wff UnifSt = (𝑓 ∈ V ↦ ((UnifSet‘𝑓) ↾t ((Base‘𝑓) × (Base‘𝑓))))

This definition is referenced by:  ussval  22583