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Definition df-ufl 22034
Description: Define the class of base sets for which the ultrafilter lemma filssufil 22044 holds. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
df-ufl UFL = {𝑥 ∣ ∀𝑓 ∈ (Fil‘𝑥)∃𝑔 ∈ (UFil‘𝑥)𝑓𝑔}
Distinct variable group:   𝑓,𝑔,𝑥

Detailed syntax breakdown of Definition df-ufl
StepHypRef Expression
1 cufl 22032 . 2 class UFL
2 vf . . . . . . 7 setvar 𝑓
32cv 1652 . . . . . 6 class 𝑓
4 vg . . . . . . 7 setvar 𝑔
54cv 1652 . . . . . 6 class 𝑔
63, 5wss 3769 . . . . 5 wff 𝑓𝑔
7 vx . . . . . . 7 setvar 𝑥
87cv 1652 . . . . . 6 class 𝑥
9 cufil 22031 . . . . . 6 class UFil
108, 9cfv 6101 . . . . 5 class (UFil‘𝑥)
116, 4, 10wrex 3090 . . . 4 wff 𝑔 ∈ (UFil‘𝑥)𝑓𝑔
12 cfil 21977 . . . . 5 class Fil
138, 12cfv 6101 . . . 4 class (Fil‘𝑥)
1411, 2, 13wral 3089 . . 3 wff 𝑓 ∈ (Fil‘𝑥)∃𝑔 ∈ (UFil‘𝑥)𝑓𝑔
1514, 7cab 2785 . 2 class {𝑥 ∣ ∀𝑓 ∈ (Fil‘𝑥)∃𝑔 ∈ (UFil‘𝑥)𝑓𝑔}
161, 15wceq 1653 1 wff UFL = {𝑥 ∣ ∀𝑓 ∈ (Fil‘𝑥)∃𝑔 ∈ (UFil‘𝑥)𝑓𝑔}
Colors of variables: wff setvar class
This definition is referenced by:  isufl  22045
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