Definition df-rtrclrec 15080

Description: The reflexive, transitive closure of a relation constructed as the union of all finite exponentiations. (Contributed by Drahflow, 12-Nov-2015.)

Assertion

Ref	Expression
df-rtrclrec	⊢ t*rec = (𝑟 ∈ V ↦ ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛))

Distinct variable group:   𝑛,𝑟

Detailed syntax breakdown of Definition df-rtrclrec

Step	Hyp	Ref	Expression
1		crtrcl 15079	. 2 class t*rec
2		vr	. . 3 setvar 𝑟
3		cvv 3464	. . 3 class V
4		vn	. . . 4 setvar 𝑛
5		cn0 12506	. . . 4 class ℕ0
6	2	cv 1539	. . . . 5 class 𝑟
7	4	cv 1539	. . . . 5 class 𝑛
8		crelexp 15043	. . . . 5 class ↑𝑟
9	6, 7, 8	co 7410	. . . 4 class (𝑟↑𝑟𝑛)
10	4, 5, 9	ciun 4972	. . 3 class ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛)
11	2, 3, 10	cmpt 5206	. 2 class (𝑟 ∈ V ↦ ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛))
12	1, 11	wceq 1540	1 wff t*rec = (𝑟 ∈ V ↦ ∪ 𝑛 ∈ ℕ0 (𝑟↑𝑟𝑛))

This definition is referenced by:  rtrclreclem1  15081  dfrtrclrec2  15082  rtrclreclem2  15083  rtrclreclem4  15085