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Definition df-chj 28297
Description: Define Hilbert lattice join. See chjval 28339 for its value and chjcl 28344 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 28342. (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 27918 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chil 27904 . . . 4 class
54cpw 4191 . . 3 class 𝒫 ℋ
62cv 1522 . . . . . 6 class 𝑥
73cv 1522 . . . . . 6 class 𝑦
86, 7cun 3605 . . . . 5 class (𝑥𝑦)
9 cort 27915 . . . . 5 class
108, 9cfv 5926 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 5926 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpt2 6692 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1523 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  28337
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