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Theorem linds2 27258
 Description: An independent set of vectors is independent as a family. (Contributed by Stefan O'Rear, 24-Feb-2015.)
Assertion
Ref Expression
linds2 LIndS LIndF

Proof of Theorem linds2
StepHypRef Expression
1 elfvdm 5757 . . . 4 LIndS LIndS
2 eqid 2436 . . . . 5
32islinds 27256 . . . 4 LIndS LIndS LIndF
41, 3syl 16 . . 3 LIndS LIndS LIndF
54ibi 233 . 2 LIndS LIndF
65simprd 450 1 LIndS LIndF
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wcel 1725   wss 3320   class class class wbr 4212   cid 4493   cdm 4878   cres 4880  cfv 5454  cbs 13469   LIndF clindf 27251  LIndSclinds 27252 This theorem is referenced by:  lindsind2  27266  lindsss  27271  f1linds  27272 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-res 4890  df-iota 5418  df-fun 5456  df-fv 5462  df-linds 27254
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