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Definition df-shft 13757
Description: Define a function shifter. This operation offsets the value argument of a function (ordinarily on a subset of ) and produces a new function on . See shftval 13764 for its value. (Contributed by NM, 20-Jul-2005.)
Assertion
Ref Expression
df-shft shift = (𝑓 ∈ V, 𝑥 ∈ ℂ ↦ {⟨𝑦, 𝑧⟩ ∣ (𝑦 ∈ ℂ ∧ (𝑦𝑥)𝑓𝑧)})
Distinct variable group:   𝑥,𝑦,𝑧,𝑓

Detailed syntax breakdown of Definition df-shft
StepHypRef Expression
1 cshi 13756 . 2 class shift
2 vf . . 3 setvar 𝑓
3 vx . . 3 setvar 𝑥
4 cvv 3190 . . 3 class V
5 cc 9894 . . 3 class
6 vy . . . . . . 7 setvar 𝑦
76cv 1479 . . . . . 6 class 𝑦
87, 5wcel 1987 . . . . 5 wff 𝑦 ∈ ℂ
93cv 1479 . . . . . . 7 class 𝑥
10 cmin 10226 . . . . . . 7 class
117, 9, 10co 6615 . . . . . 6 class (𝑦𝑥)
12 vz . . . . . . 7 setvar 𝑧
1312cv 1479 . . . . . 6 class 𝑧
142cv 1479 . . . . . 6 class 𝑓
1511, 13, 14wbr 4623 . . . . 5 wff (𝑦𝑥)𝑓𝑧
168, 15wa 384 . . . 4 wff (𝑦 ∈ ℂ ∧ (𝑦𝑥)𝑓𝑧)
1716, 6, 12copab 4682 . . 3 class {⟨𝑦, 𝑧⟩ ∣ (𝑦 ∈ ℂ ∧ (𝑦𝑥)𝑓𝑧)}
182, 3, 4, 5, 17cmpt2 6617 . 2 class (𝑓 ∈ V, 𝑥 ∈ ℂ ↦ {⟨𝑦, 𝑧⟩ ∣ (𝑦 ∈ ℂ ∧ (𝑦𝑥)𝑓𝑧)})
191, 18wceq 1480 1 wff shift = (𝑓 ∈ V, 𝑥 ∈ ℂ ↦ {⟨𝑦, 𝑧⟩ ∣ (𝑦 ∈ ℂ ∧ (𝑦𝑥)𝑓𝑧)})
Colors of variables: wff setvar class
This definition is referenced by:  shftfval  13760
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