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Definition df-sub 8128
Description: Define subtraction. Theorem subval 8147 shows its value (and describes how this definition works), Theorem subaddi 8242 relates it to addition, and Theorems subcli 8231 and resubcli 8218 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 8126 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 7808 . . 3 class
53cv 1352 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1352 . . . . . 6 class 𝑧
8 caddc 7813 . . . . . 6 class +
95, 7, 8co 5874 . . . . 5 class (𝑦 + 𝑧)
102cv 1352 . . . . 5 class 𝑥
119, 10wceq 1353 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 5829 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpo 5876 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1353 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff set class
This definition is referenced by:  subval  8147  subf  8157
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