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Definition df-sub 10265
Description: Define subtraction. Theorem subval 10269 shows its value (and describes how this definition works), theorem subaddi 10365 relates it to addition, and theorems subcli 10354 and resubcli 10340 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 10263 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 9931 . . 3 class
53cv 1481 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1481 . . . . . 6 class 𝑧
8 caddc 9936 . . . . . 6 class +
95, 7, 8co 6647 . . . . 5 class (𝑦 + 𝑧)
102cv 1481 . . . . 5 class 𝑥
119, 10wceq 1482 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 6607 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 6649 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1482 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  subval  10269  subf  10280
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