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Theorem esumex 30431
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 30430 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 ovex 6823 . . 3 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
32uniex 7100 . 2 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
41, 3eqeltri 2846 1 Σ*𝑘𝐴𝐵 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2145  Vcvv 3351   cuni 4574  cmpt 4863  (class class class)co 6793  0cc0 10138  +∞cpnf 10273  [,]cicc 12383  s cress 16065  *𝑠cxrs 16368   tsums ctsu 22149  Σ*cesum 30429
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-8 2147  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-nul 4923  ax-un 7096
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-eu 2622  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rex 3067  df-v 3353  df-sbc 3588  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-sn 4317  df-pr 4319  df-uni 4575  df-iota 5994  df-fv 6039  df-ov 6796  df-esum 30430
This theorem is referenced by:  esumcvg  30488  esumgect  30492  omssubaddlem  30701  omssubadd  30702
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