Description: Express the predicate: The limit of complex number sequence F is A , or F converges to A , with more general quantifier restrictions than clim . (Contributed by NM, 6-Jan-2007) (Revised by Mario Carneiro, 31-Jan-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | clim2.1 | |
|
clim2.2 | |
||
clim2.3 | |
||
clim2.4 | |
||
Assertion | clim2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clim2.1 | |
|
2 | clim2.2 | |
|
3 | clim2.3 | |
|
4 | clim2.4 | |
|
5 | eqidd | |
|
6 | 3 5 | clim | |
7 | 1 | uztrn2 | |
8 | 4 | eleq1d | |
9 | 4 | fvoveq1d | |
10 | 9 | breq1d | |
11 | 8 10 | anbi12d | |
12 | 7 11 | sylan2 | |
13 | 12 | anassrs | |
14 | 13 | ralbidva | |
15 | 14 | rexbidva | |
16 | 1 | rexuz3 | |
17 | 2 16 | syl | |
18 | 15 17 | bitr3d | |
19 | 18 | ralbidv | |
20 | 19 | anbi2d | |
21 | 6 20 | bitr4d | |