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Definition df-chj 30594
Description: Define Hilbert lattice join. See chjval 30636 for its value and chjcl 30641 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 30639. (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 30217 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chba 30203 . . . 4 class
54cpw 4603 . . 3 class 𝒫 ℋ
62cv 1541 . . . . . 6 class 𝑥
73cv 1541 . . . . . 6 class 𝑦
86, 7cun 3947 . . . . 5 class (𝑥𝑦)
9 cort 30214 . . . . 5 class
108, 9cfv 6544 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 6544 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpo 7411 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1542 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  30634
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