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Definition df-bj-unc 33934
Assertion
Ref Expression
df-bj-unc uncurry_ = (𝑥 ∈ V, 𝑦 ∈ V, 𝑧 ∈ V ↦ (𝑓 ∈ (𝑥 Set⟶ (𝑦 Set𝑧)) ↦ (𝑎𝑥, 𝑏𝑦 ↦ ((𝑓𝑎)‘𝑏))))
Distinct variable group:   𝑥,𝑦,𝑧,𝑎,𝑏,𝑓

Detailed syntax breakdown of Definition df-bj-unc
StepHypRef Expression
1 cunc- 33933 . 2 class uncurry_
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 vz . . 3 setvar 𝑧
5 cvv 3409 . . 3 class V
6 vf . . . 4 setvar 𝑓
72cv 1506 . . . . 5 class 𝑥
83cv 1506 . . . . . 6 class 𝑦
94cv 1506 . . . . . 6 class 𝑧
10 csethom 33923 . . . . . 6 class Set
118, 9, 10co 6970 . . . . 5 class (𝑦 Set𝑧)
127, 11, 10co 6970 . . . 4 class (𝑥 Set⟶ (𝑦 Set𝑧))
13 va . . . . 5 setvar 𝑎
14 vb . . . . 5 setvar 𝑏
1514cv 1506 . . . . . 6 class 𝑏
1613cv 1506 . . . . . . 7 class 𝑎
176cv 1506 . . . . . . 7 class 𝑓
1816, 17cfv 6182 . . . . . 6 class (𝑓𝑎)
1915, 18cfv 6182 . . . . 5 class ((𝑓𝑎)‘𝑏)
2013, 14, 7, 8, 19cmpo 6972 . . . 4 class (𝑎𝑥, 𝑏𝑦 ↦ ((𝑓𝑎)‘𝑏))
216, 12, 20cmpt 5002 . . 3 class (𝑓 ∈ (𝑥 Set⟶ (𝑦 Set𝑧)) ↦ (𝑎𝑥, 𝑏𝑦 ↦ ((𝑓𝑎)‘𝑏)))
222, 3, 4, 5, 5, 5, 21cmpt3 33921 . 2 class (𝑥 ∈ V, 𝑦 ∈ V, 𝑧 ∈ V ↦ (𝑓 ∈ (𝑥 Set⟶ (𝑦 Set𝑧)) ↦ (𝑎𝑥, 𝑏𝑦 ↦ ((𝑓𝑎)‘𝑏))))
231, 22wceq 1507 1 wff uncurry_ = (𝑥 ∈ V, 𝑦 ∈ V, 𝑧 ∈ V ↦ (𝑓 ∈ (𝑥 Set⟶ (𝑦 Set𝑧)) ↦ (𝑎𝑥, 𝑏𝑦 ↦ ((𝑓𝑎)‘𝑏))))
 Colors of variables: wff setvar class This definition is referenced by: (None)
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