Metamath Proof Explorer
Description: Join with Hilbert lattice unit. (Contributed by NM, 6-Aug-2004)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypothesis |
ch0le.1 |
|- A e. CH |
|
Assertion |
chj1i |
|- ( A vH ~H ) = ~H |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ch0le.1 |
|- A e. CH |
2 |
|
helch |
|- ~H e. CH |
3 |
1 2
|
chjcli |
|- ( A vH ~H ) e. CH |
4 |
3
|
chssii |
|- ( A vH ~H ) C_ ~H |
5 |
2 1
|
chub2i |
|- ~H C_ ( A vH ~H ) |
6 |
4 5
|
eqssi |
|- ( A vH ~H ) = ~H |