This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem chj1i

Description: Join with Hilbert lattice one. (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