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Definition df-sub 10119
Description: Define subtraction. Theorem subval 10123 shows its value (and describes how this definition works), theorem subaddi 10219 relates it to addition, and theorems subcli 10208 and resubcli 10194 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 10117 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 9790 . . 3 class
53cv 1473 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1473 . . . . . 6 class 𝑧
8 caddc 9795 . . . . . 6 class +
95, 7, 8co 6526 . . . . 5 class (𝑦 + 𝑧)
102cv 1473 . . . . 5 class 𝑥
119, 10wceq 1474 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 6487 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 6528 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1474 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  subval  10123  subf  10134
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