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Theorem seqeq1d 13921
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 13918 . 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 1542  seqcseq 13915
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-uni 4870  df-br 5110  df-opab 5172  df-mpt 5193  df-xp 5643  df-cnv 5645  df-co 5646  df-dm 5647  df-rn 5648  df-res 5649  df-ima 5650  df-pred 6257  df-iota 6452  df-fv 6508  df-ov 7364  df-frecs 8216  df-wrecs 8247  df-recs 8321  df-rdg 8360  df-seq 13916
This theorem is referenced by:  seqeq123d  13924  seqf1olem2  13957  bcval5  14227  bcn2  14228  seqshft  14979  iserex  15550  isershft  15557  isercoll2  15562  isumsplit  15733  cvgrat  15776  ntrivcvg  15790  ntrivcvgtail  15793  fprodser  15840  eftlub  15999  gsumval2a  18548  gsumsgrpccat  18658  mulgnndir  18913  geolim3  25722  fmul01lt1lem2  43916  stirlinglem7  44411  stirlinglem12  44416
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