Definition df-sub 8218

Description: Define subtraction. Theorem subval 8237 shows its value (and describes how this definition works), Theorem subaddi 8332 relates it to addition, and Theorems subcli 8321 and resubcli 8308 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 8216	. 2 class −
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cc 7896	. . 3 class ℂ
5	3	cv 1363	. . . . . 6 class 𝑦
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1363	. . . . . 6 class 𝑧
8		caddc 7901	. . . . . 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  8237  subf  8247  cndsex  14187