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Theorem cbvesumv 32011
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 2907 . 2 𝑘𝐴
3 nfcv 2907 . 2 𝑗𝐴
4 nfcv 2907 . 2 𝑘𝐵
5 nfcv 2907 . 2 𝑗𝐶
61, 2, 3, 4, 5cbvesum 32010 1 Σ*𝑗𝐴𝐵 = Σ*𝑘𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539  Σ*cesum 31995
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-nfc 2889  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-uni 4840  df-br 5075  df-opab 5137  df-mpt 5158  df-iota 6391  df-fv 6441  df-ov 7278  df-esum 31996
This theorem is referenced by:  esumcvg2  32055  omssubadd  32267  totprob  32394
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