Definition df-sub 8252

Description: Define subtraction. Theorem subval 8271 shows its value (and describes how this definition works), Theorem subaddi 8366 relates it to addition, and Theorems subcli 8355 and resubcli 8342 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

Step	Hyp	Ref	Expression
1		cmin 8250	. 2 class −
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cc 7930	. . 3 class ℂ
5	3	cv 1372	. . . . . 6 class 𝑦
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1372	. . . . . 6 class 𝑧
8		caddc 7935	. . . . . 6 class +
9	5, 7, 8	co 5951	. . . . 5 class (𝑦 + 𝑧)
10	2	cv 1372	. . . . 5 class 𝑥
11	9, 10	wceq 1373	. . . 4 wff (𝑦 + 𝑧) = 𝑥
12	11, 6, 4	crio 5905	. . 3 class (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
13	2, 3, 4, 4, 12	cmpo 5953	. 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
14	1, 13	wceq 1373	1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))

This definition is referenced by:  subval  8271  subf  8281  cndsex  14359