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Definition df-sub 6981
Description: Define subtraction. Theorem subval 7000 shows its value (and describes how this definition works), theorem subaddi 7094 relates it to addition, and theorems subcli 7083 and resubcli 7070 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
StepHypRef Expression
1 cmin 6979 . 2 class
2 vx . . 3 setvar x
3 vy . . 3 setvar y
4 cc 6709 . . 3 class
53cv 1241 . . . . . 6 class y
6 vz . . . . . . 7 setvar z
76cv 1241 . . . . . 6 class z
8 caddc 6714 . . . . . 6 class +
95, 7, 8co 5455 . . . . 5 class (y + z)
102cv 1241 . . . . 5 class x
119, 10wceq 1242 . . . 4 wff (y + z) = x
1211, 6, 4crio 5410 . . 3 class (z ℂ (y + z) = x)
132, 3, 4, 4, 12cmpt2 5457 . 2 class (x ℂ, y ℂ ↦ (z ℂ (y + z) = x))
141, 13wceq 1242 1 wff − = (x ℂ, y ℂ ↦ (z ℂ (y + z) = x))
Colors of variables: wff set class
This definition is referenced by:  subval  7000  subf  7010
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