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Theorem esumex 29418
 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 29417 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 ovex 6577 . . 3 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
32uniex 6851 . 2 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
41, 3eqeltri 2684 1 Σ*𝑘𝐴𝐵 ∈ V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1977  Vcvv 3173  ∪ cuni 4372   ↦ cmpt 4643  (class class class)co 6549  0cc0 9815  +∞cpnf 9950  [,]cicc 12049   ↾s cress 15696  ℝ*𝑠cxrs 15983   tsums ctsu 21739  Σ*cesum 29416 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-un 6847 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-v 3175  df-sbc 3403  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-sn 4126  df-pr 4128  df-uni 4373  df-iota 5768  df-fv 5812  df-ov 6552  df-esum 29417 This theorem is referenced by:  esumcvg  29475  esumgect  29479  omssubaddlem  29688  omssubadd  29689
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