Definition df-ufl 21706

Description: Define the class of base sets for which the ultrafilter lemma filssufil 21716 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

Step	Hyp	Ref	Expression
1		cufl 21704	. 2 class UFL
2		vf	. . . . . . 7 setvar f
3	2	cv 1482	. . . . . 6 class f
4		vg	. . . . . . 7 setvar g
5	4	cv 1482	. . . . . 6 class g
6	3, 5	wss 3574	. . . . 5 wff f C_ g
7		vx	. . . . . . 7 setvar x
8	7	cv 1482	. . . . . 6 class x
9		cufil 21703	. . . . . 6 class UFil
10	8, 9	cfv 5888	. . . . 5 class ( UFil ` x )
11	6, 4, 10	wrex 2913	. . . 4 wff E. g e. ( UFil ` x ) f C_ g
12		cfil 21649	. . . . 5 class Fil
13	8, 12	cfv 5888	. . . 4 class ( Fil ` x )
14	11, 2, 13	wral 2912	. . 3 wff A. f e. ( Fil ` x ) E. g e. ( UFil ` x ) f C_ g
15	14, 7	cab 2608	. 2 class { x | A. f e. ( Fil ` x ) E. g e. ( UFil ` x ) f C_ g }
16	1, 15	wceq 1483	1 wff UFL = { x | A. f e. ( Fil ` x ) E. g e. ( UFil ` x ) f C_ g }

This definition is referenced by:  isufl  21717