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Theorem s3eqd 12828
Description: Equality theorem for a length 3 word. (Contributed by Mario Carneiro, 27-Feb-2016.)
Hypotheses
Ref Expression
s2eqd.1
s2eqd.2
s3eqd.3
Assertion
Ref Expression
s3eqd

Proof of Theorem s3eqd
StepHypRef Expression
1 s2eqd.1 . . . 4
2 s2eqd.2 . . . 4
31, 2s2eqd 12827 . . 3
4 s3eqd.3 . . . 4
54s1eqd 12613 . . 3
63, 5oveq12d 6314 . 2
7 df-s3 12814 . 2
8 df-s3 12814 . 2
96, 7, 83eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  (class class class)co 6296   cconcat 12536  <"cs1 12537  <"cs2 12806  <"cs3 12807
This theorem is referenced by:  s4eqd  12829  tgcgrxfr  23909  ragcgr  24084  perpneq  24091  isperp2  24092  isperp2d  24093  footex  24095  foot  24096  perprag  24100  perpdragALT  24101  colperpexlem1  24104  lmiisolem  24161  hypcgrlem1  24164  hypcgrlem2  24165  iscgra  24169
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601  df-ov 6299  df-s1 12545  df-s2 12813  df-s3 12814
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