Description: One of the equations showing CH is an ortholattice. (This corresponds to axiom "ax-5" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | qlax.1 | |- A e. CH |
|
qlax.2 | |- B e. CH |
||
Assertion | qlax5i | |- ( A vH ( _|_ ` ( ( _|_ ` A ) vH B ) ) ) = A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlax.1 | |- A e. CH |
|
2 | qlax.2 | |- B e. CH |
|
3 | 1 2 | chdmj2i | |- ( _|_ ` ( ( _|_ ` A ) vH B ) ) = ( A i^i ( _|_ ` B ) ) |
4 | 3 | oveq2i | |- ( A vH ( _|_ ` ( ( _|_ ` A ) vH B ) ) ) = ( A vH ( A i^i ( _|_ ` B ) ) ) |
5 | 2 | choccli | |- ( _|_ ` B ) e. CH |
6 | 1 5 | chabs1i | |- ( A vH ( A i^i ( _|_ ` B ) ) ) = A |
7 | 4 6 | eqtri | |- ( A vH ( _|_ ` ( ( _|_ ` A ) vH B ) ) ) = A |