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Definition df-sub 6961
Description: Define subtraction. Theorem subval 6980 shows its value (and describes how this definition works), theorem subaddi 7074 relates it to addition, and theorems subcli 7063 and resubcli 7050 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 6959 . 2 class
2 vx . . 3 setvar x
3 vy . . 3 setvar y
4 cc 6689 . . 3 class
53cv 1241 . . . . . 6 class y
6 vz . . . . . . 7 setvar z
76cv 1241 . . . . . 6 class z
8 caddc 6694 . . . . . 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  6980  subf  6990
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