Description: Adjoint of composition of projections. Special case of Theorem 3.11(viii) of Beran p. 106. (Contributed by NM, 6-Oct-2000) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pjco.1 | |
|
pjco.2 | |
||
Assertion | pjadjcoi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pjco.1 | |
|
2 | pjco.2 | |
|
3 | 2 | pjhcli | |
4 | 1 | pjadji | |
5 | 3 4 | sylan | |
6 | 1 | pjhcli | |
7 | 2 | pjadji | |
8 | 6 7 | sylan2 | |
9 | 5 8 | eqtrd | |
10 | 1 2 | pjcoi | |
11 | 10 | oveq1d | |
12 | 11 | adantr | |
13 | 2 1 | pjcoi | |
14 | 13 | oveq2d | |
15 | 14 | adantl | |
16 | 9 12 15 | 3eqtr4d | |