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Theorem s2eqd 12647
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 12450 . . 3
3 s2eqd.2 . . . 4
43s1eqd 12450 . . 3
52, 4oveq12d 6240 . 2
6 df-s2 12633 . 2
7 df-s2 12633 . 2
85, 6, 73eqtr4g 2520 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1370  (class class class)co 6222   cconcat 12381  <"cs1 12382  <"cs2 12626
This theorem is referenced by:  s3eqd  12648  swrd2lsw  12710  efgi  16377  efgi0  16378  efgi1  16379  efgtf  16380  efgtval  16381  efgval2  16382  frgpuplem  16430
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rex 2806  df-rab 2809  df-v 3083  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-if 3906  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4209  df-br 4410  df-iota 5500  df-fv 5545  df-ov 6225  df-s1 12390  df-s2 12633
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