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Definition df-ufl 20131
Description: Define the class of base sets for which the ultrafilter lemma filssufil 20141 holds. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
df-ufl  |- UFL  =  {
x  |  A. f  e.  ( Fil `  x
) E. g  e.  ( UFil `  x
) f  C_  g }
Distinct variable group:    f, g, x

Detailed syntax breakdown of Definition df-ufl
StepHypRef Expression
1 cufl 20129 . 2  class UFL
2 vf . . . . . . 7  setvar  f
32cv 1373 . . . . . 6  class  f
4 vg . . . . . . 7  setvar  g
54cv 1373 . . . . . 6  class  g
63, 5wss 3469 . . . . 5  wff  f  C_  g
7 vx . . . . . . 7  setvar  x
87cv 1373 . . . . . 6  class  x
9 cufil 20128 . . . . . 6  class  UFil
108, 9cfv 5579 . . . . 5  class  ( UFil `  x )
116, 4, 10wrex 2808 . . . 4  wff  E. g  e.  ( UFil `  x
) f  C_  g
12 cfil 20074 . . . . 5  class  Fil
138, 12cfv 5579 . . . 4  class  ( Fil `  x )
1411, 2, 13wral 2807 . . 3  wff  A. f  e.  ( Fil `  x
) E. g  e.  ( UFil `  x
) f  C_  g
1514, 7cab 2445 . 2  class  { x  |  A. f  e.  ( Fil `  x ) E. g  e.  (
UFil `  x )
f  C_  g }
161, 15wceq 1374 1  wff UFL  =  {
x  |  A. f  e.  ( Fil `  x
) E. g  e.  ( UFil `  x
) f  C_  g }
Colors of variables: wff setvar class
This definition is referenced by:  isufl  20142
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