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Definition df-ptfin 21249
Description: Define "point-finite." (Contributed by Jeff Hankins, 21-Jan-2010.)
Assertion
Ref Expression
df-ptfin PtFin = {𝑥 ∣ ∀𝑦 𝑥{𝑧𝑥𝑦𝑧} ∈ Fin}
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-ptfin
StepHypRef Expression
1 cptfin 21246 . 2 class PtFin
2 vy . . . . . . 7 setvar 𝑦
3 vz . . . . . . 7 setvar 𝑧
42, 3wel 1988 . . . . . 6 wff 𝑦𝑧
5 vx . . . . . . 7 setvar 𝑥
65cv 1479 . . . . . 6 class 𝑥
74, 3, 6crab 2912 . . . . 5 class {𝑧𝑥𝑦𝑧}
8 cfn 7915 . . . . 5 class Fin
97, 8wcel 1987 . . . 4 wff {𝑧𝑥𝑦𝑧} ∈ Fin
106cuni 4409 . . . 4 class 𝑥
119, 2, 10wral 2908 . . 3 wff 𝑦 𝑥{𝑧𝑥𝑦𝑧} ∈ Fin
1211, 5cab 2607 . 2 class {𝑥 ∣ ∀𝑦 𝑥{𝑧𝑥𝑦𝑧} ∈ Fin}
131, 12wceq 1480 1 wff PtFin = {𝑥 ∣ ∀𝑦 𝑥{𝑧𝑥𝑦𝑧} ∈ Fin}
Colors of variables: wff setvar class
This definition is referenced by:  isptfin  21259
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