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Theorem seqeq1d 11068
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 11065 . 2  |-  ( A  =  B  ->  seq  A (  .+  ,  F
)  =  seq  B
(  .+  ,  F
) )
31, 2syl 15 1  |-  ( ph  ->  seq  A (  .+  ,  F )  =  seq  B (  .+  ,  F
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632    seq cseq 11062
This theorem is referenced by:  seqeq123d  11071  seqf1olem2  11102  bcval5  11346  bcn2  11347  seqshft  11596  iserex  12146  isershft  12153  isercoll2  12158  isumsplit  12315  cvgrat  12355  eftlub  12405  gsumval2a  14475  gsumccat  14480  mulgnndir  14605  geolim3  19735  dffprod  25422  fmul01lt1lem2  27818  stirlinglem7  27932  stirlinglem12  27937
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-mpt 4095  df-cnv 4713  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fv 5279  df-recs 6404  df-rdg 6439  df-seq 11063
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