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Definition df-chj 28057
 Description: Define Hilbert lattice join. See chjval 28099 for its value and chjcl 28104 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 Cℋ; see sshjcl 28102. (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 27678 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 chil 27664 . . . 4 class
54cpw 4136 . . 3 class 𝒫 ℋ
62cv 1479 . . . . . 6 class 𝑥
73cv 1479 . . . . . 6 class 𝑦
86, 7cun 3558 . . . . 5 class (𝑥𝑦)
9 cort 27675 . . . . 5 class
108, 9cfv 5857 . . . 4 class (⊥‘(𝑥𝑦))
1110, 9cfv 5857 . . 3 class (⊥‘(⊥‘(𝑥𝑦)))
122, 3, 5, 5, 11cmpt2 6617 . 2 class (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
131, 12wceq 1480 1 wff = (𝑥 ∈ 𝒫 ℋ, 𝑦 ∈ 𝒫 ℋ ↦ (⊥‘(⊥‘(𝑥𝑦))))
 Colors of variables: wff setvar class This definition is referenced by:  sshjval  28097
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