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Definition df-sub 10147
 Description: Define subtraction. Theorem subval 10151 shows its value (and describes how this definition works), theorem subaddi 10247 relates it to addition, and theorems subcli 10236 and resubcli 10222 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 10145 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 9813 . . 3 class
53cv 1474 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1474 . . . . . 6 class 𝑧
8 caddc 9818 . . . . . 6 class +
95, 7, 8co 6549 . . . . 5 class (𝑦 + 𝑧)
102cv 1474 . . . . 5 class 𝑥
119, 10wceq 1475 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 6510 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 6551 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1475 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
 Colors of variables: wff setvar class This definition is referenced by:  subval  10151  subf  10162
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