Description: Join with lattice zero in CH . (Contributed by NM, 15-Oct-1999) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | ch0le.1 | |- A e. CH |
|
| Assertion | chj0i | |- ( A vH 0H ) = A |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ch0le.1 | |- A e. CH |
|
| 2 | h0elch | |- 0H e. CH |
|
| 3 | 1 2 | chjvali | |- ( A vH 0H ) = ( _|_ ` ( _|_ ` ( A u. 0H ) ) ) |
| 4 | 1 | ch0lei | |- 0H C_ A |
| 5 | ssequn2 | |- ( 0H C_ A <-> ( A u. 0H ) = A ) |
|
| 6 | 4 5 | mpbi | |- ( A u. 0H ) = A |
| 7 | 6 | fveq2i | |- ( _|_ ` ( A u. 0H ) ) = ( _|_ ` A ) |
| 8 | 7 | fveq2i | |- ( _|_ ` ( _|_ ` ( A u. 0H ) ) ) = ( _|_ ` ( _|_ ` A ) ) |
| 9 | 1 | pjococi | |- ( _|_ ` ( _|_ ` A ) ) = A |
| 10 | 3 8 9 | 3eqtri | |- ( A vH 0H ) = A |