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Theorem s1eqd 11440
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 11439 . 2  |-  ( A  =  B  ->  <" A ">  =  <" B "> )
31, 2syl 15 1  |-  ( ph  ->  <" A ">  =  <" B "> )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   <"cs1 11405
This theorem is referenced by:  swrds1  11473  s2eqd  11512  s3eqd  11513  s4eqd  11514  s5eqd  11515  s6eqd  11516  s7eqd  11517  s8eqd  11518  frmdgsum  14484  efgredlemc  15054  vrgpval  15076  vrgpinv  15078  frgpup2  15085  frgpup3lem  15086  psgnunilem5  27417
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-s1 11411
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