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Theorem seqeq3d 11054
Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.)
Hypothesis
Ref Expression
seqeqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
seqeq3d  |-  ( ph  ->  seq  M (  .+  ,  A )  =  seq  M (  .+  ,  B
) )

Proof of Theorem seqeq3d
StepHypRef Expression
1 seqeqd.1 . 2  |-  ( ph  ->  A  =  B )
2 seqeq3 11051 . 2  |-  ( A  =  B  ->  seq  M (  .+  ,  A
)  =  seq  M
(  .+  ,  B
) )
31, 2syl 15 1  |-  ( ph  ->  seq  M (  .+  ,  A )  =  seq  M (  .+  ,  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    seq cseq 11046
This theorem is referenced by:  seqeq123d  11055  seqf1olem2  11086  seqf1o  11087  expval  11106  sumeq1f  12161  sumeq2w  12165  cbvsum  12168  summo  12190  fsum  12193  geomulcvg  12332  gsumvalx  14451  mulgval  14569  gsumval3eu  15190  gsumval3  15191  gsumzres  15194  gsumzf1o  15196  elovolmr  18835  ovolctb  18849  ovoliunlem3  18863  ovoliunnul  18866  ovolshftlem1  18868  voliunlem3  18909  voliun  18911  uniioombllem2  18938  vitalilem4  18966  vitalilem5  18967  dvnfval  19271  radcnv0  19792  radcnvlt1  19794  radcnvle  19796  psercn  19802  pserdvlem2  19804  abelthlem1  19807  abelthlem3  19809  logtayl  20007  atantayl2  20234  atantayl3  20235  lgsval  20539  lgsval4  20555  lgsneg  20558  lgsmod  20560  dchrmusumlema  20642  dchrisum0lema  20663  gxval  20925  stirlinglem5  27827
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-ral 2548  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-opab 4078  df-mpt 4079  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fv 5263  df-ov 5861  df-oprab 5862  df-mpt2 5863  df-recs 6388  df-rdg 6423  df-seq 11047
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