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Definition df-sub 10670
 Description: Define subtraction. Theorem subval 10675 shows its value (and describes how this definition works), theorem subaddi 10772 relates it to addition, and theorems subcli 10761 and resubcli 10747 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 10668 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 10331 . . 3 class
53cv 1506 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1506 . . . . . 6 class 𝑧
8 caddc 10336 . . . . . 6 class +
95, 7, 8co 6974 . . . . 5 class (𝑦 + 𝑧)
102cv 1506 . . . . 5 class 𝑥
119, 10wceq 1507 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 6934 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpo 6976 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1507 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
 Colors of variables: wff setvar class This definition is referenced by:  subval  10675  subf  10686
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