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Definition df-sub 10306
Description: Define subtraction. Theorem subval 10310 shows its value (and describes how this definition works), theorem subaddi 10406 relates it to addition, and theorems subcli 10395 and resubcli 10381 prove its closure laws. (Contributed by NM, 26-Nov-1994.)
Assertion
Ref Expression
df-sub − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-sub
StepHypRef Expression
1 cmin 10304 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 9972 . . 3 class
53cv 1522 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1522 . . . . . 6 class 𝑧
8 caddc 9977 . . . . . 6 class +
95, 7, 8co 6690 . . . . 5 class (𝑦 + 𝑧)
102cv 1522 . . . . 5 class 𝑥
119, 10wceq 1523 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 6650 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 6692 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1523 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  subval  10310  subf  10321
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