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Definition df-chj 31192
Description: Define Hilbert lattice join. See chjval 31234 for its value and chjcl 31239 for its closure law. Note that we define it over all Hilbert space subsets to allow proving more general theorems. Even for general subsets the join belongs to C; see sshjcl 31237. (Contributed by NM, 1-Nov-2000.) (New usage is discouraged.)
Assertion
Ref Expression
df-chj = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-chj
StepHypRef Expression
1 chj 30815 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chba 30801 . . . 4 class
54cpw 4604 . . 3 class 𝒫 ℋ
62cv 1532 . . . . . 6 class 𝑥
73cv 1532 . . . . . 6 class 𝑦
86, 7cun 3942 . . . . 5 class (𝑥𝑦)
9 cort 30812 . . . . 5 class
108, 9cfv 6549 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 6549 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpo 7421 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1533 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  31232
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