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 | chlej1i | |- ( A C_ B -> ( A vH C ) C_ ( B vH C ) ) |
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 | shlej1i | |- ( A C_ B -> ( A vH C ) C_ ( B vH C ) ) |