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Mirrors > Home > MPE Home > Th. List > df-rtrclrec | Structured version Visualization version GIF version |
Description: The reflexive, transitive closure of a relation constructed as the union of all finite exponentiations. (Contributed by Drahflow, 12-Nov-2015.) |
Ref | Expression |
---|---|
df-rtrclrec | ⊢ t*rec = (𝑟 ∈ V ↦ ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crtrcl 13643 | . 2 class t*rec | |
2 | vr | . . 3 setvar 𝑟 | |
3 | cvv 3173 | . . 3 class V | |
4 | vn | . . . 4 setvar 𝑛 | |
5 | cn0 11169 | . . . 4 class ℕ0 | |
6 | 2 | cv 1474 | . . . . 5 class 𝑟 |
7 | 4 | cv 1474 | . . . . 5 class 𝑛 |
8 | crelexp 13608 | . . . . 5 class ↑𝑟 | |
9 | 6, 7, 8 | co 6549 | . . . 4 class (𝑟↑𝑟𝑛) |
10 | 4, 5, 9 | ciun 4455 | . . 3 class ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛) |
11 | 2, 3, 10 | cmpt 4643 | . 2 class (𝑟 ∈ V ↦ ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛)) |
12 | 1, 11 | wceq 1475 | 1 wff t*rec = (𝑟 ∈ V ↦ ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛)) |
Colors of variables: wff setvar class |
This definition is referenced by: dfrtrclrec2 13645 rtrclreclem1 13646 rtrclreclem2 13647 rtrclreclem4 13649 |
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