Metamath Proof Explorer


Theorem chj1i

Description: Join with Hilbert lattice unit. (Contributed by NM, 6-Aug-2004) (New usage is discouraged.)

Ref Expression
Hypothesis ch0le.1 𝐴C
Assertion chj1i ( 𝐴 ℋ ) = ℋ

Proof

Step Hyp Ref Expression
1 ch0le.1 𝐴C
2 helch ℋ ∈ C
3 1 2 chjcli ( 𝐴 ℋ ) ∈ C
4 3 chssii ( 𝐴 ℋ ) ⊆ ℋ
5 2 1 chub2i ℋ ⊆ ( 𝐴 ℋ )
6 4 5 eqssi ( 𝐴 ℋ ) = ℋ