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Definition df-ulm 24131

Description: Define the uniform convergence of a sequence of functions. Here

is a sequence of functions

defined on

and

is a function on

, and for every

there is a

such that the functions

for

are all uniformly within

on the domain

. Compare with df-clim 14219. (Contributed by Mario Carneiro, 26-Feb-2015.)

**Assertion**
Ref	Expression
df-ulm	$/\$ $/\$

**Detailed syntax breakdown of Definition df-ulm**
Step	Hyp	Ref	Expression
1		culm 24130	. 2
2		vs	. . 3
3		cvv 3200	. . 3
4		vn	. . . . . . . . 9
5	4	cv 1482	. . . . . . . 8
6		cuz 11687	. . . . . . . 8
7	5, 6	cfv 5888	. . . . . . 7
8		cc 9934	. . . . . . . 8
9	2	cv 1482	. . . . . . . 8
10		cmap 7857	. . . . . . . 8
11	8, 9, 10	co 6650	. . . . . . 7
12		vf	. . . . . . . 8
13	12	cv 1482	. . . . . . 7
14	7, 11, 13	wf 5884	. . . . . 6
15		vy	. . . . . . . 8
16	15	cv 1482	. . . . . . 7
17	9, 8, 16	wf 5884	. . . . . 6
18		vz	. . . . . . . . . . . . . . 15
19	18	cv 1482	. . . . . . . . . . . . . 14
20		vk	. . . . . . . . . . . . . . . 16
21	20	cv 1482	. . . . . . . . . . . . . . 15
22	21, 13	cfv 5888	. . . . . . . . . . . . . 14
23	19, 22	cfv 5888	. . . . . . . . . . . . 13
24	19, 16	cfv 5888	. . . . . . . . . . . . 13
25		cmin 10266	. . . . . . . . . . . . 13
26	23, 24, 25	co 6650	. . . . . . . . . . . 12
27		cabs 13974	. . . . . . . . . . . 12
28	26, 27	cfv 5888	. . . . . . . . . . 11
29		vx	. . . . . . . . . . . 12
30	29	cv 1482	. . . . . . . . . . 11
31		clt 10074	. . . . . . . . . . 11
32	28, 30, 31	wbr 4653	. . . . . . . . . 10
33	32, 18, 9	wral 2912	. . . . . . . . 9
34		vj	. . . . . . . . . . 11
35	34	cv 1482	. . . . . . . . . 10
36	35, 6	cfv 5888	. . . . . . . . 9
37	33, 20, 36	wral 2912	. . . . . . . 8
38	37, 34, 7	wrex 2913	. . . . . . 7
39		crp 11832	. . . . . . 7
40	38, 29, 39	wral 2912	. . . . . 6
41	14, 17, 40	w3a 1037	. . . . 5 $/\$ $/\$
42		cz 11377	. . . . 5
43	41, 4, 42	wrex 2913	. . . 4 $/\$ $/\$
44	43, 12, 15	copab 4712	. . 3 $/\$ $/\$
45	2, 3, 44	cmpt 4729	. 2 $/\$ $/\$
46	1, 45	wceq 1483	1 $/\$ $/\$

Colors of variables: wff setvar class

This definition is referenced by: ulmrel 24132 ulmval 24134