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Definition df-hvsub 30492
Description: Define vector subtraction. See hvsubvali 30541 for its value and hvsubcli 30542 for its closure. (Contributed by NM, 6-Jun-2008.) (New usage is discouraged.)
Assertion
Ref Expression
df-hvsub โˆ’โ„Ž = (๐‘ฅ โˆˆ โ„‹, ๐‘ฆ โˆˆ โ„‹ โ†ฆ (๐‘ฅ +โ„Ž (-1 ยทโ„Ž ๐‘ฆ)))
Distinct variable group:   ๐‘ฅ,๐‘ฆ

Detailed syntax breakdown of Definition df-hvsub
StepHypRef Expression
1 cmv 30446 . 2 class โˆ’โ„Ž
2 vx . . 3 setvar ๐‘ฅ
3 vy . . 3 setvar ๐‘ฆ
4 chba 30440 . . 3 class โ„‹
52cv 1539 . . . 4 class ๐‘ฅ
6 c1 11114 . . . . . 6 class 1
76cneg 11450 . . . . 5 class -1
83cv 1539 . . . . 5 class ๐‘ฆ
9 csm 30442 . . . . 5 class ยทโ„Ž
107, 8, 9co 7412 . . . 4 class (-1 ยทโ„Ž ๐‘ฆ)
11 cva 30441 . . . 4 class +โ„Ž
125, 10, 11co 7412 . . 3 class (๐‘ฅ +โ„Ž (-1 ยทโ„Ž ๐‘ฆ))
132, 3, 4, 4, 12cmpo 7414 . 2 class (๐‘ฅ โˆˆ โ„‹, ๐‘ฆ โˆˆ โ„‹ โ†ฆ (๐‘ฅ +โ„Ž (-1 ยทโ„Ž ๐‘ฆ)))
141, 13wceq 1540 1 wff โˆ’โ„Ž = (๐‘ฅ โˆˆ โ„‹, ๐‘ฆ โˆˆ โ„‹ โ†ฆ (๐‘ฅ +โ„Ž (-1 ยทโ„Ž ๐‘ฆ)))
Colors of variables: wff setvar class
This definition is referenced by:  h2hvs  30498  hvsubf  30536  hvsubval  30537
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