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Definition df-ufl 17613
Description: Define the class of base sets for which the ultrafilter lemma filssufil 17623 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 17611 . 2  class UFL
2 vf . . . . . . 7  set  f
32cv 1631 . . . . . 6  class  f
4 vg . . . . . . 7  set  g
54cv 1631 . . . . . 6  class  g
63, 5wss 3165 . . . . 5  wff  f  C_  g
7 vx . . . . . . 7  set  x
87cv 1631 . . . . . 6  class  x
9 cufil 17610 . . . . . 6  class  UFil
108, 9cfv 5271 . . . . 5  class  ( UFil `  x )
116, 4, 10wrex 2557 . . . 4  wff  E. g  e.  ( UFil `  x
) f  C_  g
12 cfil 17556 . . . . 5  class  Fil
138, 12cfv 5271 . . . 4  class  ( Fil `  x )
1411, 2, 13wral 2556 . . 3  wff  A. f  e.  ( Fil `  x
) E. g  e.  ( UFil `  x
) f  C_  g
1514, 7cab 2282 . 2  class  { x  |  A. f  e.  ( Fil `  x ) E. g  e.  (
UFil `  x )
f  C_  g }
161, 15wceq 1632 1  wff UFL  =  {
x  |  A. f  e.  ( Fil `  x
) E. g  e.  ( UFil `  x
) f  C_  g }
Colors of variables: wff set class
This definition is referenced by:  isufl  17624
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