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Theorem seqeq1d 13363
Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.)
Hypothesis
Ref Expression
seqeqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
seqeq1d (𝜑 → seq𝐴( + , 𝐹) = seq𝐵( + , 𝐹))

Proof of Theorem seqeq1d
StepHypRef Expression
1 seqeqd.1 . 2 (𝜑𝐴 = 𝐵)
2 seqeq1 13360 . 2 (𝐴 = 𝐵 → seq𝐴( + , 𝐹) = seq𝐵( + , 𝐹))
31, 2syl 17 1 (𝜑 → seq𝐴( + , 𝐹) = seq𝐵( + , 𝐹))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1528  seqcseq 13357
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ral 3140  df-rex 3141  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564  df-uni 4831  df-br 5058  df-opab 5120  df-mpt 5138  df-xp 5554  df-cnv 5556  df-dm 5558  df-rn 5559  df-res 5560  df-ima 5561  df-pred 6141  df-iota 6307  df-fv 6356  df-wrecs 7936  df-recs 7997  df-rdg 8035  df-seq 13358
This theorem is referenced by:  seqeq123d  13366  seqf1olem2  13398  bcval5  13666  bcn2  13667  seqshft  14432  iserex  15001  isershft  15008  isercoll2  15013  isumsplit  15183  cvgrat  15227  ntrivcvg  15241  ntrivcvgtail  15244  fprodser  15291  eftlub  15450  gsumval2a  17883  gsumsgrpccat  17992  gsumccatOLD  17993  mulgnndir  18194  geolim3  24855  fmul01lt1lem2  41742  stirlinglem7  42242  stirlinglem12  42247
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