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Definition df-chj 30029
Description: Define Hilbert lattice join. See chjval 30071 for its value and chjcl 30076 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 30074. (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 29652 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chba 29638 . . . 4 class
54cpw 4558 . . 3 class 𝒫 ℋ
62cv 1540 . . . . . 6 class 𝑥
73cv 1540 . . . . . 6 class 𝑦
86, 7cun 3906 . . . . 5 class (𝑥𝑦)
9 cort 29649 . . . . 5 class
108, 9cfv 6491 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 6491 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpo 7351 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1541 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  30069
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