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Theorem nfesum1 30436
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 30424 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 nfcv 2912 . . . 4 𝑘(ℝ*𝑠s (0[,]+∞))
3 nfcv 2912 . . . 4 𝑘 tsums
4 nfmpt1 4879 . . . 4 𝑘(𝑘𝐴𝐵)
52, 3, 4nfov 6820 . . 3 𝑘((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
65nfuni 4578 . 2 𝑘 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
71, 6nfcxfr 2910 1 𝑘Σ*𝑘𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:  wnfc 2899   cuni 4572  cmpt 4861  (class class class)co 6792  0cc0 10137  +∞cpnf 10272  [,]cicc 12382  s cress 16064  *𝑠cxrs 16367   tsums ctsu 22148  Σ*cesum 30423
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ral 3065  df-rex 3066  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-uni 4573  df-br 4785  df-opab 4845  df-mpt 4862  df-iota 5994  df-fv 6039  df-ov 6795  df-esum 30424
This theorem is referenced by:  esumfsup  30466  esum2d  30489  oms0  30693  omssubadd  30696
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