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Theorem esumex 31516
 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 31515 . 2 Σ*𝑘𝐴𝐵 = ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵))
2 ovex 7183 . . 3 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
32uniex 7465 . 2 ((ℝ*𝑠s (0[,]+∞)) tsums (𝑘𝐴𝐵)) ∈ V
41, 3eqeltri 2848 1 Σ*𝑘𝐴𝐵 ∈ V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2111  Vcvv 3409  ∪ cuni 4798   ↦ cmpt 5112  (class class class)co 7150  0cc0 10575  +∞cpnf 10710  [,]cicc 12782   ↾s cress 16542  ℝ*𝑠cxrs 16831   tsums ctsu 22826  Σ*cesum 31514 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2729  ax-sep 5169  ax-nul 5176  ax-un 7459 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-fal 1551  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2557  df-eu 2588  df-clab 2736  df-cleq 2750  df-clel 2830  df-ral 3075  df-rex 3076  df-v 3411  df-sbc 3697  df-dif 3861  df-un 3863  df-in 3865  df-ss 3875  df-nul 4226  df-sn 4523  df-pr 4525  df-uni 4799  df-iota 6294  df-fv 6343  df-ov 7153  df-esum 31515 This theorem is referenced by:  esumcvg  31573  esumgect  31577  omssubaddlem  31785  omssubadd  31786
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