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Theorem s2eqd 11826
 Description: Equality theorem for a doubleton word. (Contributed by Mario Carneiro, 27-Feb-2016.)
Hypotheses
Ref Expression
s2eqd.1
s2eqd.2
Assertion
Ref Expression
s2eqd

Proof of Theorem s2eqd
StepHypRef Expression
1 s2eqd.1 . . . 4
21s1eqd 11754 . . 3
3 s2eqd.2 . . . 4
43s1eqd 11754 . . 3
52, 4oveq12d 6099 . 2 concat concat
6 df-s2 11812 . 2 concat
7 df-s2 11812 . 2 concat
85, 6, 73eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652  (class class class)co 6081   concat cconcat 11718  cs1 11719  cs2 11805 This theorem is referenced by:  s3eqd  11827  efgi  15351  efgi0  15352  efgi1  15353  efgtf  15354  efgtval  15355  efgval2  15356  frgpuplem  15404 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-ov 6084  df-s1 11725  df-s2 11812
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