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Definition df-tail 17278
 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
StepHypRef Expression
1 ctail 17276 . 2 class tail
2 vr . . 3 setvar 𝑟
3 cdir 17275 . . 3 class DirRel
4 vx . . . 4 setvar 𝑥
52cv 1522 . . . . . 6 class 𝑟
65cuni 4468 . . . . 5 class 𝑟
76cuni 4468 . . . 4 class 𝑟
84cv 1522 . . . . . 6 class 𝑥
98csn 4210 . . . . 5 class {𝑥}
105, 9cima 5146 . . . 4 class (𝑟 “ {𝑥})
114, 7, 10cmpt 4762 . . 3 class (𝑥 𝑟 ↦ (𝑟 “ {𝑥}))
122, 3, 11cmpt 4762 . 2 class (𝑟 ∈ DirRel ↦ (𝑥 𝑟 ↦ (𝑟 “ {𝑥})))
131, 12wceq 1523 1 wff tail = (𝑟 ∈ DirRel ↦ (𝑥 𝑟 ↦ (𝑟 “ {𝑥})))
 Colors of variables: wff setvar class This definition is referenced by:  tailfval  32492
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