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Definition df-sub 10470
Description: Define subtraction. Theorem subval 10474 shows its value (and describes how this definition works), theorem subaddi 10570 relates it to addition, and theorems subcli 10559 and resubcli 10545 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 10468 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 10136 . . 3 class
53cv 1630 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1630 . . . . . 6 class 𝑧
8 caddc 10141 . . . . . 6 class +
95, 7, 8co 6793 . . . . 5 class (𝑦 + 𝑧)
102cv 1630 . . . . 5 class 𝑥
119, 10wceq 1631 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 6753 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 6795 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1631 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  subval  10474  subf  10485
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