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Theorem s1eqd 12563
Description: Equality theorem for a singleton word. (Contributed by Mario Carneiro, 26-Feb-2016.)
Hypothesis
Ref Expression
s1eqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
s1eqd  |-  ( ph  ->  <" A ">  =  <" B "> )

Proof of Theorem s1eqd
StepHypRef Expression
1 s1eqd.1 . 2  |-  ( ph  ->  A  =  B )
2 s1eq 12562 . 2  |-  ( A  =  B  ->  <" A ">  =  <" B "> )
31, 2syl 16 1  |-  ( ph  ->  <" A ">  =  <" B "> )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1374   <"cs1 12490
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-rex 2813  df-rab 2816  df-v 3108  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-if 3933  df-sn 4021  df-pr 4023  df-op 4027  df-uni 4239  df-br 4441  df-iota 5542  df-fv 5587  df-s1 12498
This theorem is referenced by:  swrds1  12626  swrdlsw  12627  swrdccatwrd  12643  s2eqd  12777  s3eqd  12778  s4eqd  12779  s5eqd  12780  s6eqd  12781  s7eqd  12782  s8eqd  12783  frmdgsum  15846  psgnunilem5  16308  efgredlemc  16552  vrgpval  16574  vrgpinv  16576  frgpup2  16583  frgpup3lem  16584  iwrdsplit  27952  sseqval  27953  sseqf  27957  sseqp1  27960  signsvtn0  28153
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