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Definition df-chj 29418
Description: Define Hilbert lattice join. See chjval 29460 for its value and chjcl 29465 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 29463. (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 29041 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chba 29027 . . . 4 class
54cpw 4528 . . 3 class 𝒫 ℋ
62cv 1542 . . . . . 6 class 𝑥
73cv 1542 . . . . . 6 class 𝑦
86, 7cun 3879 . . . . 5 class (𝑥𝑦)
9 cort 29038 . . . . 5 class
108, 9cfv 6398 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 6398 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpo 7234 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1543 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  29458
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