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Theorem esumex 33776
Description: An extended sum is a set by definition. (Contributed by Thierry Arnoux, 5-Sep-2017.)
Assertion
Ref Expression
esumex Σ*𝑘𝐴𝐵 ∈ V

Proof of Theorem esumex
StepHypRef Expression
1 df-esum 33775 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 ovex 7452 . . 3 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
32uniex 7747 . 2 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
41, 3eqeltri 2821 1 Σ*𝑘𝐴𝐵 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2098  Vcvv 3461   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 33774
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-ext 2696  ax-sep 5300  ax-nul 5307  ax-un 7741
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ne 2930  df-v 3463  df-dif 3947  df-un 3949  df-ss 3961  df-nul 4323  df-sn 4631  df-pr 4633  df-uni 4910  df-iota 6501  df-fv 6557  df-ov 7422  df-esum 33775
This theorem is referenced by:  esumcvg  33833  esumgect  33837  omssubaddlem  34047  omssubadd  34048
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