Description: The zero operator between two normed complex vector spaces. (Contributed by NM, 28-Nov-2007) (Revised by Mario Carneiro, 16-Nov-2013) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | 0oval.1 | |
|
0oval.6 | |
||
0oval.0 | |
||
Assertion | 0ofval | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0oval.1 | |
|
2 | 0oval.6 | |
|
3 | 0oval.0 | |
|
4 | fveq2 | |
|
5 | 4 1 | eqtr4di | |
6 | 5 | xpeq1d | |
7 | fveq2 | |
|
8 | 7 2 | eqtr4di | |
9 | 8 | sneqd | |
10 | 9 | xpeq2d | |
11 | df-0o | |
|
12 | 1 | fvexi | |
13 | snex | |
|
14 | 12 13 | xpex | |
15 | 6 10 11 14 | ovmpo | |
16 | 3 15 | eqtrid | |