Definition df-sub 11466

Description: Define subtraction. Theorem subval 11471 shows its value (and describes how this definition works), Theorem subaddi 11568 relates it to addition, and Theorems subcli 11557 and resubcli 11543 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 11464	. 2 class −
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cc 11125	. . 3 class ℂ
5	3	cv 1539	. . . . . 6 class 𝑦
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1539	. . . . . 6 class 𝑧
8		caddc 11130	. . . . . 6 class +
9	5, 7, 8	co 7403	. . . . 5 class (𝑦 + 𝑧)
10	2	cv 1539	. . . . 5 class 𝑥
11	9, 10	wceq 1540	. . . 4 wff (𝑦 + 𝑧) = 𝑥
12	11, 6, 4	crio 7359	. . 3 class (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
13	2, 3, 4, 4, 12	cmpo 7405	. 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
14	1, 13	wceq 1540	1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))

This definition is referenced by:  subval  11471  subf  11482  sn-subf  42418