Definition df-sub 10872

Description: Define subtraction. Theorem subval 10877 shows its value (and describes how this definition works), theorem subaddi 10973 relates it to addition, and theorems subcli 10962 and resubcli 10948 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 10870	. 2 class −
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cc 10535	. . 3 class ℂ
5	3	cv 1536	. . . . . 6 class 𝑦
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1536	. . . . . 6 class 𝑧
8		caddc 10540	. . . . . 6 class +
9	5, 7, 8	co 7156	. . . . 5 class (𝑦 + 𝑧)
10	2	cv 1536	. . . . 5 class 𝑥
11	9, 10	wceq 1537	. . . 4 wff (𝑦 + 𝑧) = 𝑥
12	11, 6, 4	crio 7113	. . 3 class (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥)
13	2, 3, 4, 4, 12	cmpo 7158	. 2 class (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))
14	1, 13	wceq 1537	1 wff − = (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (℩𝑧 ∈ ℂ (𝑦 + 𝑧) = 𝑥))

This definition is referenced by:  subval  10877  subf  10888