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Theorem seqeq1d 11052
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 11049 . 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 1623    seq cseq 11046
This theorem is referenced by:  seqeq123d  11055  seqf1olem2  11086  bcval5  11330  bcn2  11331  seqshft  11580  iserex  12130  isershft  12137  isercoll2  12142  isumsplit  12299  cvgrat  12339  eftlub  12389  gsumval2a  14459  gsumccat  14464  mulgnndir  14589  geolim3  19719  dffprod  25319  fmul01lt1lem2  27715  stirlinglem7  27829  stirlinglem12  27834
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-recs 6388  df-rdg 6423  df-seq 11047
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