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Theorem nfesum1 34041
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 34029 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 nfcv 2905 . . . 4 𝑘(ℝ*𝑠s (0[,]+∞))
3 nfcv 2905 . . . 4 𝑘 tsums
4 nfmpt1 5250 . . . 4 𝑘(𝑘𝐴𝐵)
52, 3, 4nfov 7461 . . 3 𝑘((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
65nfuni 4914 . 2 𝑘 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
71, 6nfcxfr 2903 1 𝑘Σ*𝑘𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2890   cuni 4907  cmpt 5225  (class class class)co 7431  0cc0 11155  +∞cpnf 11292  [,]cicc 13390  s cress 17274  *𝑠cxrs 17545   tsums ctsu 24134  Σ*cesum 34028
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-mpt 5226  df-iota 6514  df-fv 6569  df-ov 7434  df-esum 34029
This theorem is referenced by:  esumfsup  34071  esum2d  34094  oms0  34299  omssubadd  34302
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