Description: The function applying continuous extension to a given function f . (Contributed by Thierry Arnoux, 1-Dec-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | cnextval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unieq | |
|
2 | 1 | oveq2d | |
3 | fveq2 | |
|
4 | 3 | fveq1d | |
5 | fveq2 | |
|
6 | 5 | fveq1d | |
7 | 6 | oveq1d | |
8 | 7 | oveq2d | |
9 | 8 | fveq1d | |
10 | 9 | xpeq2d | |
11 | 4 10 | iuneq12d | |
12 | 2 11 | mpteq12dv | |
13 | unieq | |
|
14 | 13 | oveq1d | |
15 | oveq1 | |
|
16 | 15 | fveq1d | |
17 | 16 | xpeq2d | |
18 | 17 | iuneq2d | |
19 | 14 18 | mpteq12dv | |
20 | df-cnext | |
|
21 | ovex | |
|
22 | 21 | mptex | |
23 | 12 19 20 22 | ovmpo | |