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Definition df-sub 10861
Description: Define subtraction. Theorem subval 10866 shows its value (and describes how this definition works), theorem subaddi 10962 relates it to addition, and theorems subcli 10951 and resubcli 10937 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 10859 . 2 class
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cc 10524 . . 3 class
53cv 1527 . . . . . 6 class 𝑦
6 vz . . . . . . 7 setvar 𝑧
76cv 1527 . . . . . 6 class 𝑧
8 caddc 10529 . . . . . 6 class +
95, 7, 8co 7145 . . . . 5 class (𝑦 + 𝑧)
102cv 1527 . . . . 5 class 𝑥
119, 10wceq 1528 . . . 4 wff (𝑦 + 𝑧) = 𝑥
1211, 6, 4crio 7102 . . 3 class (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
132, 3, 4, 4, 12cmpo 7147 . 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
141, 13wceq 1528 1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  subval  10866  subf  10877
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