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Theorem cbvesumv 31359
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 2982 . 2 𝑘𝐴
3 nfcv 2982 . 2 𝑗𝐴
4 nfcv 2982 . 2 𝑘𝐵
5 nfcv 2982 . 2 𝑗𝐶
61, 2, 3, 4, 5cbvesum 31358 1 Σ*𝑗𝐴𝐵 = Σ*𝑘𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538  Σ*cesum 31343
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5053  df-opab 5115  df-mpt 5133  df-iota 6302  df-fv 6351  df-ov 7152  df-esum 31344
This theorem is referenced by:  esumcvg2  31403  omssubadd  31615  totprob  31742
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