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Definition df-cur 7545
Description: Define the currying of 𝐹, which splits a function of two arguments into a function of the first argument, producing a function over the second argument. (Contributed by Mario Carneiro, 7-Jan-2017.)
Assertion
Ref Expression
df-cur curry 𝐹 = (𝑥 ∈ dom dom 𝐹 ↦ {⟨𝑦, 𝑧⟩ ∣ ⟨𝑥, 𝑦𝐹𝑧})
Distinct variable group:   𝑥,𝑦,𝑧,𝐹

Detailed syntax breakdown of Definition df-cur
StepHypRef Expression
1 cF . . 3 class 𝐹
21ccur 7543 . 2 class curry 𝐹
3 vx . . 3 setvar 𝑥
41cdm 5249 . . . 4 class dom 𝐹
54cdm 5249 . . 3 class dom dom 𝐹
63cv 1630 . . . . . 6 class 𝑥
7 vy . . . . . . 7 setvar 𝑦
87cv 1630 . . . . . 6 class 𝑦
96, 8cop 4322 . . . . 5 class 𝑥, 𝑦
10 vz . . . . . 6 setvar 𝑧
1110cv 1630 . . . . 5 class 𝑧
129, 11, 1wbr 4786 . . . 4 wff 𝑥, 𝑦𝐹𝑧
1312, 7, 10copab 4846 . . 3 class {⟨𝑦, 𝑧⟩ ∣ ⟨𝑥, 𝑦𝐹𝑧}
143, 5, 13cmpt 4863 . 2 class (𝑥 ∈ dom dom 𝐹 ↦ {⟨𝑦, 𝑧⟩ ∣ ⟨𝑥, 𝑦𝐹𝑧})
152, 14wceq 1631 1 wff curry 𝐹 = (𝑥 ∈ dom dom 𝐹 ↦ {⟨𝑦, 𝑧⟩ ∣ ⟨𝑥, 𝑦𝐹𝑧})
Colors of variables: wff setvar class
This definition is referenced by:  mpt2curryd  7547  cureq  33718  curf  33720  curunc  33724  matunitlindf  33740
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