Description: Hilbert lattice join distributes over itself. (Contributed by NM, 29-Apr-2006) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | chj12.1 | |- A e. CH |
|
chj12.2 | |- B e. CH |
||
chj12.3 | |- C e. CH |
||
Assertion | chjjdiri | |- ( ( A vH B ) vH C ) = ( ( A vH C ) vH ( B vH C ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chj12.1 | |- A e. CH |
|
2 | chj12.2 | |- B e. CH |
|
3 | chj12.3 | |- C e. CH |
|
4 | 3 | chjidmi | |- ( C vH C ) = C |
5 | 4 | oveq2i | |- ( ( A vH B ) vH ( C vH C ) ) = ( ( A vH B ) vH C ) |
6 | 1 2 3 3 | chj4i | |- ( ( A vH B ) vH ( C vH C ) ) = ( ( A vH C ) vH ( B vH C ) ) |
7 | 5 6 | eqtr3i | |- ( ( A vH B ) vH C ) = ( ( A vH C ) vH ( B vH C ) ) |