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Theorem seqeq1d 11284
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
seqeq1d  |-  ( ph  ->  seq  A (  .+  ,  F )  =  seq  B (  .+  ,  F
) )

Proof of Theorem seqeq1d
StepHypRef Expression
1 seqeqd.1 . 2  |-  ( ph  ->  A  =  B )
2 seqeq1 11281 . 2  |-  ( A  =  B  ->  seq  A (  .+  ,  F
)  =  seq  B
(  .+  ,  F
) )
31, 2syl 16 1  |-  ( ph  ->  seq  A (  .+  ,  F )  =  seq  B (  .+  ,  F
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    seq cseq 11278
This theorem is referenced by:  seqeq123d  11287  seqf1olem2  11318  bcval5  11564  bcn2  11565  seqshft  11855  iserex  12405  isershft  12412  isercoll2  12417  isumsplit  12575  cvgrat  12615  eftlub  12665  gsumval2a  14737  gsumccat  14742  mulgnndir  14867  geolim3  20209  ntrivcvg  25178  ntrivcvgtail  25181  fprodser  25228  fmul01lt1lem2  27582  stirlinglem7  27696  stirlinglem12  27701
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 2385
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 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-opab 4227  df-mpt 4228  df-cnv 4845  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850  df-iota 5377  df-fv 5421  df-recs 6592  df-rdg 6627  df-seq 11279
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