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 ∈ Cℋ |
|
Assertion |
chj1i |
⊢ ( 𝐴 ∨ℋ ℋ ) = ℋ |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ch0le.1 |
⊢ 𝐴 ∈ Cℋ |
2 |
|
helch |
⊢ ℋ ∈ Cℋ |
3 |
1 2
|
chjcli |
⊢ ( 𝐴 ∨ℋ ℋ ) ∈ Cℋ |
4 |
3
|
chssii |
⊢ ( 𝐴 ∨ℋ ℋ ) ⊆ ℋ |
5 |
2 1
|
chub2i |
⊢ ℋ ⊆ ( 𝐴 ∨ℋ ℋ ) |
6 |
4 5
|
eqssi |
⊢ ( 𝐴 ∨ℋ ℋ ) = ℋ |