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Theorem nfesum1 30087
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 30075 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 nfcv 2763 . . . 4 𝑘(ℝ*𝑠s (0[,]+∞))
3 nfcv 2763 . . . 4 𝑘 tsums
4 nfmpt1 4745 . . . 4 𝑘(𝑘𝐴𝐵)
52, 3, 4nfov 6673 . . 3 𝑘((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
65nfuni 4440 . 2 𝑘 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
71, 6nfcxfr 2761 1 𝑘Σ*𝑘𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2750   cuni 4434  cmpt 4727  (class class class)co 6647  0cc0 9933  +∞cpnf 10068  [,]cicc 12175  s cress 15852  *𝑠cxrs 16154   tsums ctsu 21923  Σ*cesum 30074
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-10 2018  ax-11 2033  ax-12 2046  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1485  df-ex 1704  df-nf 1709  df-sb 1880  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2752  df-ral 2916  df-rex 2917  df-rab 2920  df-v 3200  df-dif 3575  df-un 3577  df-in 3579  df-ss 3586  df-nul 3914  df-if 4085  df-sn 4176  df-pr 4178  df-op 4182  df-uni 4435  df-br 4652  df-opab 4711  df-mpt 4728  df-iota 5849  df-fv 5894  df-ov 6650  df-esum 30075
This theorem is referenced by:  esumfsup  30117  esum2d  30140  oms0  30344  omssubadd  30347
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