Definition df-tail 18103

Description: Define the tail function for directed sets. (Contributed by Jeff Hankins, 25-Nov-2009.)

Assertion

Ref	Expression
df-tail	⊢ tail = (𝑟 ∈ DirRel ↦ (𝑥 ∈ ∪ ∪ 𝑟 ↦ (𝑟 “ {𝑥})))

Distinct variable group:   𝑥,𝑟

Detailed syntax breakdown of Definition df-tail

Step	Hyp	Ref	Expression
1		ctail 18101	. 2 class tail
2		vr	. . 3 setvar 𝑟
3		cdir 18100	. . 3 class DirRel
4		vx	. . . 4 setvar 𝑥
5	2	cv 1542	. . . . . 6 class 𝑟
6	5	cuni 4819	. . . . 5 class ∪ 𝑟
7	6	cuni 4819	. . . 4 class ∪ ∪ 𝑟
8	4	cv 1542	. . . . . 6 class 𝑥
9	8	csn 4541	. . . . 5 class {𝑥}
10	5, 9	cima 5554	. . . 4 class (𝑟 “ {𝑥})
11	4, 7, 10	cmpt 5135	. . 3 class (𝑥 ∈ ∪ ∪ 𝑟 ↦ (𝑟 “ {𝑥}))
12	2, 3, 11	cmpt 5135	. 2 class (𝑟 ∈ DirRel ↦ (𝑥 ∈ ∪ ∪ 𝑟 ↦ (𝑟 “ {𝑥})))
13	1, 12	wceq 1543	1 wff tail = (𝑟 ∈ DirRel ↦ (𝑥 ∈ ∪ ∪ 𝑟 ↦ (𝑟 “ {𝑥})))

This definition is referenced by:  tailfval  34298