Description: Add join to both sides of a Hilbert lattice ordering. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ch0le.1 | |- A e. CH |
|
| chjcl.2 | |- B e. CH |
||
| chlub.1 | |- C e. CH |
||
| Assertion | chlej2i | |- ( A C_ B -> ( C vH A ) C_ ( C vH B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ch0le.1 | |- A e. CH |
|
| 2 | chjcl.2 | |- B e. CH |
|
| 3 | chlub.1 | |- C e. CH |
|
| 4 | 1 | chshii | |- A e. SH |
| 5 | 2 | chshii | |- B e. SH |
| 6 | 3 | chshii | |- C e. SH |
| 7 | 4 5 6 | shlej2i | |- ( A C_ B -> ( C vH A ) C_ ( C vH B ) ) |