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Theorem cbvesumv 32682
Description: Change bound variable in an extended sum. (Contributed by Thierry Arnoux, 19-Jun-2017.)
Hypothesis
Ref Expression
cbvesum.1 (𝑗 = 𝑘𝐵 = 𝐶)
Assertion
Ref Expression
cbvesumv Σ*𝑗𝐴𝐵 = Σ*𝑘𝐴𝐶
Distinct variable groups:   𝑗,𝑘,𝐴   𝐵,𝑘   𝐶,𝑗
Allowed substitution hints:   𝐵(𝑗)   𝐶(𝑘)

Proof of Theorem cbvesumv
StepHypRef Expression
1 cbvesum.1 . 2 (𝑗 = 𝑘𝐵 = 𝐶)
2 nfcv 2908 . 2 𝑘𝐴
3 nfcv 2908 . 2 𝑗𝐴
4 nfcv 2908 . 2 𝑘𝐵
5 nfcv 2908 . 2 𝑗𝐶
61, 2, 3, 4, 5cbvesum 32681 1 Σ*𝑗𝐴𝐵 = Σ*𝑘𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  Σ*cesum 32666
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-10 2138  ax-11 2155  ax-12 2172  ax-ext 2708
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-nf 1787  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-nfc 2890  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-if 4492  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4871  df-br 5111  df-opab 5173  df-mpt 5194  df-iota 6453  df-fv 6509  df-ov 7365  df-esum 32667
This theorem is referenced by:  esumcvg2  32726  omssubadd  32940  totprob  33067
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