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Definition df-sub 10556
Description: Define subtraction. Theorem subval 10560 shows its value (and describes how this definition works), theorem subaddi 10656 relates it to addition, and theorems subcli 10645 and resubcli 10631 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 10554 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 10222 . . 3 class
53cv 1636 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1636 . . . . . 6 class 𝑧
8 caddc 10227 . . . . . 6 class +
95, 7, 8co 6877 . . . . 5 class (𝑦 + 𝑧)
102cv 1636 . . . . 5 class 𝑥
119, 10wceq 1637 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 6837 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 6879 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1637 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  subval  10560  subf  10571
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