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Theorem s1eq 11753
 Description: Equality theorem for a singleton word. (Contributed by Mario Carneiro, 26-Feb-2016.)
Assertion
Ref Expression
s1eq

Proof of Theorem s1eq
StepHypRef Expression
1 fveq2 5728 . . . 4
21opeq2d 3991 . . 3
32sneqd 3827 . 2
4 df-s1 11725 . 2
5 df-s1 11725 . 2
63, 4, 53eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652  csn 3814  cop 3817   cid 4493  cfv 5454  cc0 8990  cs1 11719 This theorem is referenced by:  s1eqd  11754  wrdind  11791  revs1  11797  vrmdval  14802  frgpup3lem  15409  vdegp1ci  21708 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-s1 11725
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