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

Theorem dvhvscaval 34738
 Description: The scalar product operation for the constructed full vector space H. (Contributed by NM, 20-Nov-2013.)
Hypothesis
Ref Expression
dvhvscaval.s
Assertion
Ref Expression
dvhvscaval
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem dvhvscaval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fveq1 5878 . . 3
2 coeq1 4997 . . 3
31, 2opeq12d 4166 . 2
4 fveq2 5879 . . . 4
54fveq2d 5883 . . 3
6 fveq2 5879 . . . 4
76coeq2d 5002 . . 3
85, 7opeq12d 4166 . 2
9 dvhvscaval.s . . 3
109dvhvscacbv 34737 . 2
11 opex 4664 . 2
123, 8, 10, 11ovmpt2 6451 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376   wceq 1452   wcel 1904  cop 3965   cxp 4837   ccom 4843  cfv 5589  (class class class)co 6308   cmpt2 6310  c1st 6810  c2nd 6811 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-iota 5553  df-fun 5591  df-fv 5597  df-ov 6311  df-oprab 6312  df-mpt2 6313 This theorem is referenced by:  dvhvsca  34740  dvhopspN  34754
 Copyright terms: Public domain W3C validator