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Definition df-chj 28741
Description: Define Hilbert lattice join. See chjval 28783 for its value and chjcl 28788 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 28786. (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 28362 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chba 28348 . . . 4 class
54cpw 4378 . . 3 class 𝒫 ℋ
62cv 1600 . . . . . 6 class 𝑥
73cv 1600 . . . . . 6 class 𝑦
86, 7cun 3789 . . . . 5 class (𝑥𝑦)
9 cort 28359 . . . . 5 class
108, 9cfv 6135 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 6135 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpt2 6924 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1601 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  28781
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