Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-rest Structured version   Visualization version   GIF version

Definition df-rest 15906
 Description: Function returning the subspace topology induced by the topology 𝑦 and the set 𝑥. (Contributed by FL, 20-Sep-2010.) (Revised by Mario Carneiro, 1-May-2015.)
Assertion
Ref Expression
df-rest t = (𝑗 ∈ V, 𝑥 ∈ V ↦ ran (𝑦𝑗 ↦ (𝑦𝑥)))
Distinct variable group:   𝑥,𝑗,𝑦

Detailed syntax breakdown of Definition df-rest
StepHypRef Expression
1 crest 15904 . 2 class t
2 vj . . 3 setvar 𝑗
3 vx . . 3 setvar 𝑥
4 cvv 3173 . . 3 class V
5 vy . . . . 5 setvar 𝑦
62cv 1474 . . . . 5 class 𝑗
75cv 1474 . . . . . 6 class 𝑦
83cv 1474 . . . . . 6 class 𝑥
97, 8cin 3539 . . . . 5 class (𝑦𝑥)
105, 6, 9cmpt 4643 . . . 4 class (𝑦𝑗 ↦ (𝑦𝑥))
1110crn 5039 . . 3 class ran (𝑦𝑗 ↦ (𝑦𝑥))
122, 3, 4, 4, 11cmpt2 6551 . 2 class (𝑗 ∈ V, 𝑥 ∈ V ↦ ran (𝑦𝑗 ↦ (𝑦𝑥)))
131, 12wceq 1475 1 wff t = (𝑗 ∈ V, 𝑥 ∈ V ↦ ran (𝑦𝑗 ↦ (𝑦𝑥)))
 Colors of variables: wff setvar class This definition is referenced by:  restfn  15908  restval  15910  bj-restsnid  32221
 Copyright terms: Public domain W3C validator