Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  hvsubval Unicode version

Theorem hvsubval 21596
 Description: Value of vector subtraction. (Contributed by NM, 5-Sep-1999.) (Revised by Mario Carneiro, 23-Dec-2013.) (New usage is discouraged.)
Assertion
Ref Expression
hvsubval

Proof of Theorem hvsubval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq1 5865 . 2
2 oveq2 5866 . . 3
32oveq2d 5874 . 2
4 df-hvsub 21551 . 2
5 ovex 5883 . 2
61, 3, 4, 5ovmpt2 5983 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1623   wcel 1684  (class class class)co 5858  c1 8738  cneg 9038  chil 21499   cva 21500   csm 21501   cmv 21505 This theorem is referenced by:  hvsubcl  21597  hvsubvali  21600  hvsubid  21605  hvnegid  21606  hv2neg  21607  hvaddsubval  21612  hvsub4  21616  hvaddsub12  21617  hvpncan  21618  hvaddsubass  21620  hvsubass  21623  hvsubdistr1  21628  hvsubdistr2  21629  hvsubcan  21653  hvsub0  21655  his2sub  21671  hhph  21757  shsubcl  21800  shsel3  21894  honegsubi  22376  lnopsubi  22554  lnfnsubi  22626  superpos  22934  cdj1i  23013 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-iota 5219  df-fun 5257  df-fv 5263  df-ov 5861  df-oprab 5862  df-mpt2 5863  df-hvsub 21551
 Copyright terms: Public domain W3C validator