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Definition df-chj 28508
Description: Define Hilbert lattice join. See chjval 28550 for its value and chjcl 28555 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 28553. (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 28129 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chil 28115 . . . 4 class
54cpw 4298 . . 3 class 𝒫 ℋ
62cv 1630 . . . . . 6 class 𝑥
73cv 1630 . . . . . 6 class 𝑦
86, 7cun 3721 . . . . 5 class (𝑥𝑦)
9 cort 28126 . . . . 5 class
108, 9cfv 6030 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 6030 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpt2 6797 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1631 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  28548
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