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Theorem s4eqd 12829
 Description: Equality theorem for a length 4 word. (Contributed by Mario Carneiro, 27-Feb-2016.)
Hypotheses
Ref Expression
s2eqd.1
s2eqd.2
s3eqd.3
s4eqd.4
Assertion
Ref Expression
s4eqd

Proof of Theorem s4eqd
StepHypRef Expression
1 s2eqd.1 . . . 4
2 s2eqd.2 . . . 4
3 s3eqd.3 . . . 4
41, 2, 3s3eqd 12828 . . 3
5 s4eqd.4 . . . 4
65s1eqd 12613 . . 3
74, 6oveq12d 6314 . 2
8 df-s4 12815 . 2
9 df-s4 12815 . 2
107, 8, 93eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  (class class class)co 6296   cconcat 12536  <"cs1 12537  <"cs3 12807  <"cs4 12808 This theorem is referenced by:  s5eqd  12830 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  df-s4 12815
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