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Definition df-sub 11478
Description: Define subtraction. Theorem subval 11483 shows its value (and describes how this definition works), Theorem subaddi 11579 relates it to addition, and Theorems subcli 11568 and resubcli 11554 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 11476 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 11138 . . 3 class
53cv 1532 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1532 . . . . . 6 class 𝑧
8 caddc 11143 . . . . . 6 class +
95, 7, 8co 7419 . . . . 5 class (𝑦 + 𝑧)
102cv 1532 . . . . 5 class 𝑥
119, 10wceq 1533 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 7374 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpo 7421 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1533 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  subval  11483  subf  11494  sn-subf  42118
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