Description: The orthomodular law. Remark in Kalmbach p. 22. (Contributed by NM, 12-Jun-2006) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pjoml2.1 | |- A e. CH |
|
pjoml2.2 | |- B e. CH |
||
Assertion | pjoml5i | |- ( A vH ( ( _|_ ` A ) i^i ( A vH B ) ) ) = ( A vH B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pjoml2.1 | |- A e. CH |
|
2 | pjoml2.2 | |- B e. CH |
|
3 | 1 2 | chub1i | |- A C_ ( A vH B ) |
4 | 1 2 | chjcli | |- ( A vH B ) e. CH |
5 | 1 4 | pjoml2i | |- ( A C_ ( A vH B ) -> ( A vH ( ( _|_ ` A ) i^i ( A vH B ) ) ) = ( A vH B ) ) |
6 | 3 5 | ax-mp | |- ( A vH ( ( _|_ ` A ) i^i ( A vH B ) ) ) = ( A vH B ) |