Definition df-sub 8340

Description: Define subtraction. Theorem subval 8359 shows its value (and describes how this definition works), Theorem subaddi 8454 relates it to addition, and Theorems subcli 8443 and resubcli 8430 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 8338	. 2 class −
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cc 8018	. . 3 class ℂ
5	3	cv 1394	. . . . . 6 class 𝑦
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1394	. . . . . 6 class 𝑧
8		caddc 8023	. . . . . 6 class +
9	5, 7, 8	co 6011	. . . . 5 class (𝑦 + 𝑧)
10	2	cv 1394	. . . . 5 class 𝑥
11	9, 10	wceq 1395	. . . 4 wff (𝑦 + 𝑧) = 𝑥
12	11, 6, 4	crio 5963	. . 3 class (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
13	2, 3, 4, 4, 12	cmpo 6013	. 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
14	1, 13	wceq 1395	1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))

This definition is referenced by:  subval  8359  subf  8369  cndsex  14554