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Theorem vscaid 12549
Description: Utility theorem: index-independent form of scalar product df-vsca 12497. (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 12497 . 2  |-  .s  = Slot  6
2 6nn 9043 . 2  |-  6  e.  NN
31, 2ndxid 12440 1  |-  .s  = Slot  ( .s `  ndx )
Colors of variables: wff set class
Syntax hints:    = wceq 1348   ` cfv 5198   6c6 8933   ndxcnx 12413  Slot cslot 12415   .scvsca 12484
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-13 2143  ax-14 2144  ax-ext 2152  ax-sep 4107  ax-pow 4160  ax-pr 4194  ax-un 4418  ax-cnex 7865  ax-resscn 7866  ax-1re 7868  ax-addrcl 7871
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-eu 2022  df-mo 2023  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-rex 2454  df-v 2732  df-sbc 2956  df-un 3125  df-in 3127  df-ss 3134  df-pw 3568  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-int 3832  df-br 3990  df-opab 4051  df-mpt 4052  df-id 4278  df-xp 4617  df-rel 4618  df-cnv 4619  df-co 4620  df-dm 4621  df-rn 4622  df-res 4623  df-iota 5160  df-fun 5200  df-fv 5206  df-ov 5856  df-inn 8879  df-2 8937  df-3 8938  df-4 8939  df-5 8940  df-6 8941  df-ndx 12419  df-slot 12420  df-vsca 12497
This theorem is referenced by: (None)
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