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Definition df-sub 7247
Description: Define subtraction. Theorem subval 7266 shows its value (and describes how this definition works), theorem subaddi 7361 relates it to addition, and theorems subcli 7350 and resubcli 7337 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 7245 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 6945 . . 3 class
53cv 1258 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1258 . . . . . 6 class 𝑧
8 caddc 6950 . . . . . 6 class +
95, 7, 8co 5540 . . . . 5 class (𝑦 + 𝑧)
102cv 1258 . . . . 5 class 𝑥
119, 10wceq 1259 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 5495 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 5542 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1259 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff set class
This definition is referenced by:  subval  7266  subf  7276
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