Description: The projection subspace of the difference between two projectors. Part 2 of Theorem 1 of AkhiezerGlazman p. 65. (Contributed by NM, 3-Jun-2006) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pjclem1.1 | |
|
pjclem1.2 | |
||
Assertion | pjcmul2i | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pjclem1.1 | |
|
2 | pjclem1.2 | |
|
3 | 1 2 | pjclem4 | |
4 | pjmfn | |
|
5 | 1 2 | chincli | |
6 | fnfvelrn | |
|
7 | 4 5 6 | mp2an | |
8 | eleq1 | |
|
9 | 7 8 | mpbiri | |
10 | 1 2 | pjcmul1i | |
11 | 9 10 | sylibr | |
12 | 3 11 | impbii | |