Description: A rearrangement of Hilbert lattice join. (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 | chj12i | |- ( A vH ( B vH C ) ) = ( B vH ( A 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 | 1 2 | chjcomi | |- ( A vH B ) = ( B vH A ) |
5 | 4 | oveq1i | |- ( ( A vH B ) vH C ) = ( ( B vH A ) vH C ) |
6 | 1 2 3 | chjassi | |- ( ( A vH B ) vH C ) = ( A vH ( B vH C ) ) |
7 | 2 1 3 | chjassi | |- ( ( B vH A ) vH C ) = ( B vH ( A vH C ) ) |
8 | 5 6 7 | 3eqtr3i | |- ( A vH ( B vH C ) ) = ( B vH ( A vH C ) ) |