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Theorem vscaid 12635
Description: Utility theorem: index-independent form of scalar product df-vsca 12572. (Contributed by Mario Carneiro, 2-Oct-2013.) (Revised by Mario Carneiro, 19-Jun-2014.)
Assertion
Ref Expression
vscaid  |-  .s  = Slot  ( .s `  ndx )

Proof of Theorem vscaid
StepHypRef Expression
1 df-vsca 12572 . 2  |-  .s  = Slot  6
2 6nn 9102 . 2  |-  6  e.  NN
31, 2ndxid 12504 1  |-  .s  = Slot  ( .s `  ndx )
Colors of variables: wff set class
Syntax hints:    = wceq 1364   ` cfv 5231   6c6 8992   ndxcnx 12477  Slot cslot 12479   .scvsca 12559
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4189  ax-pr 4224  ax-un 4448  ax-cnex 7920  ax-resscn 7921  ax-1re 7923  ax-addrcl 7926
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-sbc 2978  df-un 3148  df-in 3150  df-ss 3157  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-int 3860  df-br 4019  df-opab 4080  df-mpt 4081  df-id 4308  df-xp 4647  df-rel 4648  df-cnv 4649  df-co 4650  df-dm 4651  df-rn 4652  df-res 4653  df-iota 5193  df-fun 5233  df-fv 5239  df-ov 5894  df-inn 8938  df-2 8996  df-3 8997  df-4 8998  df-5 8999  df-6 9000  df-ndx 12483  df-slot 12484  df-vsca 12572
This theorem is referenced by: (None)
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