Definition df-sub 8287

Description: Define subtraction. Theorem subval 8306 shows its value (and describes how this definition works), Theorem subaddi 8401 relates it to addition, and Theorems subcli 8390 and resubcli 8377 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 8285	. 2 class −
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cc 7965	. . 3 class ℂ
5	3	cv 1374	. . . . . 6 class 𝑦
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1374	. . . . . 6 class 𝑧
8		caddc 7970	. . . . . 6 class +
9	5, 7, 8	co 5974	. . . . 5 class (𝑦 + 𝑧)
10	2	cv 1374	. . . . 5 class 𝑥
11	9, 10	wceq 1375	. . . 4 wff (𝑦 + 𝑧) = 𝑥
12	11, 6, 4	crio 5926	. . 3 class (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
13	2, 3, 4, 4, 12	cmpo 5976	. 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
14	1, 13	wceq 1375	1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))

This definition is referenced by:  subval  8306  subf  8316  cndsex  14482