Definition df-sub 8216

Description: Define subtraction. Theorem subval 8235 shows its value (and describes how this definition works), Theorem subaddi 8330 relates it to addition, and Theorems subcli 8319 and resubcli 8306 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 8214	. 2 class −
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cc 7894	. . 3 class ℂ
5	3	cv 1363	. . . . . 6 class 𝑦
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1363	. . . . . 6 class 𝑧
8		caddc 7899	. . . . . 6 class +
9	5, 7, 8	co 5925	. . . . 5 class (𝑦 + 𝑧)
10	2	cv 1363	. . . . 5 class 𝑥
11	9, 10	wceq 1364	. . . 4 wff (𝑦 + 𝑧) = 𝑥
12	11, 6, 4	crio 5879	. . 3 class (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
13	2, 3, 4, 4, 12	cmpo 5927	. 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
14	1, 13	wceq 1364	1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))

This definition is referenced by:  subval  8235  subf  8245  cndsex  14185