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Theorem s1eqd 12313
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 12312 . 2  |-  ( A  =  B  ->  <" A ">  =  <" B "> )
31, 2syl 16 1  |-  ( ph  ->  <" A ">  =  <" B "> )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1369   <"cs1 12245
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-rex 2742  df-rab 2745  df-v 2995  df-dif 3352  df-un 3354  df-in 3356  df-ss 3363  df-nul 3659  df-if 3813  df-sn 3899  df-pr 3901  df-op 3905  df-uni 4113  df-br 4314  df-iota 5402  df-fv 5447  df-s1 12253
This theorem is referenced by:  swrds1  12366  swrdlsw  12367  swrdccatwrd  12383  s2eqd  12510  s3eqd  12511  s4eqd  12512  s5eqd  12513  s6eqd  12514  s7eqd  12515  s8eqd  12516  frmdgsum  15561  psgnunilem5  16021  efgredlemc  16263  vrgpval  16285  vrgpinv  16287  frgpup2  16294  frgpup3lem  16295  iwrdsplit  26792  sseqval  26793  sseqf  26797  sseqp1  26800  signsvtn0  26993
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