Description: A projector is a bounded linear operator. (Contributed by NM, 3-Jun-2006) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | pjhmop.1 | |
|
Assertion | pjbdlni | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pjhmop.1 | |
|
2 | 1 | pjlnopi | |
3 | 2fveq3 | |
|
4 | 3 | eleq1d | |
5 | 1 | pjnmopi | |
6 | 1re | |
|
7 | 5 6 | eqeltrdi | |
8 | 7 | adantl | |
9 | df-h0op | |
|
10 | 9 | fveq2i | |
11 | nmop0 | |
|
12 | 10 11 | eqtr3i | |
13 | 0re | |
|
14 | 12 13 | eqeltri | |
15 | 14 | a1i | |
16 | 4 8 15 | pm2.61ne | |
17 | 1 16 | ax-mp | |
18 | elbdop2 | |
|
19 | 2 17 18 | mpbir2an | |