HSE Home Hilbert Space Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HSE Home  >  Th. List  >  df-hvsub Structured version   Visualization version   GIF version

Definition df-hvsub 30262
Description: Define vector subtraction. See hvsubvali 30311 for its value and hvsubcli 30312 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 30216 . 2 class โˆ’โ„Ž
2 vx . . 3 setvar ๐‘ฅ
3 vy . . 3 setvar ๐‘ฆ
4 chba 30210 . . 3 class โ„‹
52cv 1540 . . . 4 class ๐‘ฅ
6 c1 11113 . . . . . 6 class 1
76cneg 11447 . . . . 5 class -1
83cv 1540 . . . . 5 class ๐‘ฆ
9 csm 30212 . . . . 5 class ยทโ„Ž
107, 8, 9co 7411 . . . 4 class (-1 ยทโ„Ž ๐‘ฆ)
11 cva 30211 . . . 4 class +โ„Ž
125, 10, 11co 7411 . . 3 class (๐‘ฅ +โ„Ž (-1 ยทโ„Ž ๐‘ฆ))
132, 3, 4, 4, 12cmpo 7413 . 2 class (๐‘ฅ โˆˆ โ„‹, ๐‘ฆ โˆˆ โ„‹ โ†ฆ (๐‘ฅ +โ„Ž (-1 ยทโ„Ž ๐‘ฆ)))
141, 13wceq 1541 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  30268  hvsubf  30306  hvsubval  30307
  Copyright terms: Public domain W3C validator