Description: De Morgan's law for meet in a Hilbert lattice. (Contributed by NM, 21-Jun-2004) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ch0le.1 | |- A e. CH |
|
chjcl.2 | |- B e. CH |
||
Assertion | chdmm2i | |- ( _|_ ` ( ( _|_ ` A ) i^i B ) ) = ( A vH ( _|_ ` B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ch0le.1 | |- A e. CH |
|
2 | chjcl.2 | |- B e. CH |
|
3 | 1 | choccli | |- ( _|_ ` A ) e. CH |
4 | 3 2 | chdmm1i | |- ( _|_ ` ( ( _|_ ` A ) i^i B ) ) = ( ( _|_ ` ( _|_ ` A ) ) vH ( _|_ ` B ) ) |
5 | 1 | pjococi | |- ( _|_ ` ( _|_ ` A ) ) = A |
6 | 5 | oveq1i | |- ( ( _|_ ` ( _|_ ` A ) ) vH ( _|_ ` B ) ) = ( A vH ( _|_ ` B ) ) |
7 | 4 6 | eqtri | |- ( _|_ ` ( ( _|_ ` A ) i^i B ) ) = ( A vH ( _|_ ` B ) ) |