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Definition df-sub 7182
Description: Define subtraction. Theorem subval 7201 shows its value (and describes how this definition works), theorem subaddi 7296 relates it to addition, and theorems subcli 7285 and resubcli 7272 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 7180 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 6885 . . 3 class
53cv 1242 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1242 . . . . . 6 class 𝑧
8 caddc 6890 . . . . . 6 class +
95, 7, 8co 5512 . . . . 5 class (𝑦 + 𝑧)
102cv 1242 . . . . 5 class 𝑥
119, 10wceq 1243 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 5467 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpt2 5514 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1243 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff set class
This definition is referenced by:  subval  7201  subf  7211
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