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Theorem nfesum1 33790
Description: Bound-variable hypothesis builder for extended sum. (Contributed by Thierry Arnoux, 19-Oct-2017.)
Hypothesis
Ref Expression
nfesum1.1 𝑘𝐴
Assertion
Ref Expression
nfesum1 𝑘Σ*𝑘𝐴𝐵

Proof of Theorem nfesum1
StepHypRef Expression
1 df-esum 33778 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 nfcv 2891 . . . 4 𝑘(ℝ*𝑠s (0[,]+∞))
3 nfcv 2891 . . . 4 𝑘 tsums
4 nfmpt1 5257 . . . 4 𝑘(𝑘𝐴𝐵)
52, 3, 4nfov 7449 . . 3 𝑘((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
65nfuni 4916 . 2 𝑘 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
71, 6nfcxfr 2889 1 𝑘Σ*𝑘𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2875   cuni 4909  cmpt 5232  (class class class)co 7419  0cc0 11140  +∞cpnf 11277  [,]cicc 13362  s cress 17212  *𝑠cxrs 17485   tsums ctsu 24074  Σ*cesum 33777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-ral 3051  df-rex 3060  df-rab 3419  df-v 3463  df-dif 3947  df-un 3949  df-ss 3961  df-nul 4323  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4910  df-br 5150  df-opab 5212  df-mpt 5233  df-iota 6501  df-fv 6557  df-ov 7422  df-esum 33778
This theorem is referenced by:  esumfsup  33820  esum2d  33843  oms0  34048  omssubadd  34051
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