Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dvhvaddval Structured version   Unicode version

 Description: The vector sum operation for the constructed full vector space H. (Contributed by NM, 26-Oct-2013.)
Hypothesis
Ref Expression
Assertion
Ref Expression
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fveq2 5872 . . . 4
21coeq1d 5007 . . 3
3 fveq2 5872 . . . 4
43oveq1d 6311 . . 3
52, 4opeq12d 4189 . 2
6 fveq2 5872 . . . 4
76coeq2d 5008 . . 3
8 fveq2 5872 . . . 4
98oveq2d 6312 . . 3
107, 9opeq12d 4189 . 2
13 opex 4677 . 2
145, 10, 12, 13ovmpt2 6437 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   wcel 1867  cop 3999   cxp 4843   ccom 4849  cfv 5592  (class class class)co 6296   cmpt2 6298  c1st 6796  c2nd 6797 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-sbc 3297  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-br 4418  df-opab 4476  df-id 4760  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-iota 5556  df-fun 5594  df-fv 5600  df-ov 6299  df-oprab 6300  df-mpt2 6301 This theorem is referenced by:  dvhvadd  34413  dvhopaddN  34435
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