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Theorem s1eqd 11785
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 11784 . 2  |-  ( A  =  B  ->  <" A ">  =  <" B "> )
31, 2syl 16 1  |-  ( ph  ->  <" A ">  =  <" B "> )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653   <"cs1 11750
This theorem is referenced by:  swrds1  11818  s2eqd  11857  s3eqd  11858  s4eqd  11859  s5eqd  11860  s6eqd  11861  s7eqd  11862  s8eqd  11863  frmdgsum  14838  efgredlemc  15408  vrgpval  15430  vrgpinv  15432  frgpup2  15439  frgpup3lem  15440  psgnunilem5  27432
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-iota 5447  df-fv 5491  df-s1 11756
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