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Theorem seqeq3d 11294
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 11291 . 2  |-  ( A  =  B  ->  seq  M (  .+  ,  A
)  =  seq  M
(  .+  ,  B
) )
31, 2syl 16 1  |-  ( ph  ->  seq  M (  .+  ,  A )  =  seq  M (  .+  ,  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    seq cseq 11286
This theorem is referenced by:  seqeq123d  11295  seqf1olem2  11326  seqf1o  11327  seqof2  11344  expval  11347  sumeq1f  12445  sumeq2w  12449  cbvsum  12452  summo  12474  fsum  12477  geomulcvg  12616  gsumvalx  14737  mulgval  14855  gsumval3eu  15476  gsumval3  15477  gsumzres  15480  gsumzf1o  15482  elovolmr  19333  ovolctb  19347  ovoliunlem3  19361  ovoliunnul  19364  ovolshftlem1  19366  voliunlem3  19407  voliun  19409  uniioombllem2  19436  vitalilem4  19464  vitalilem5  19465  dvnfval  19769  mtestbdd  20282  radcnv0  20293  radcnvlt1  20295  radcnvle  20297  psercn  20303  pserdvlem2  20305  abelthlem1  20308  abelthlem3  20310  logtayl  20512  atantayl2  20739  atantayl3  20740  lgsval  21045  lgsval4  21061  lgsneg  21064  lgsmod  21066  dchrmusumlema  21148  dchrisum0lema  21169  gxval  21807  lgamgulm2  24781  lgamcvglem  24785  prodeq1f  25195  prodeq2w  25199  prodmo  25223  fprod  25228  faclim  25321  ovoliunnfl  26155  voliunnfl  26157  stirlinglem5  27702
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-uni 3984  df-br 4181  df-opab 4235  df-mpt 4236  df-cnv 4853  df-dm 4855  df-rn 4856  df-res 4857  df-ima 4858  df-iota 5385  df-fv 5429  df-ov 6051  df-oprab 6052  df-mpt2 6053  df-recs 6600  df-rdg 6635  df-seq 11287
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