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Theorem esumex 26623
Description: An extended sum is a set by definition. (Contributed by Thierry Arnoux, 5-Sep-2017.)
Assertion
Ref Expression
esumex  |- Σ* k  e.  A B  e.  _V

Proof of Theorem esumex
StepHypRef Expression
1 df-esum 26622 . 2  |- Σ* k  e.  A B  =  U. (
( RR*ss  ( 0 [,] +oo ) ) tsums  ( k  e.  A  |->  B ) )
2 ovex 6218 . . 3  |-  ( (
RR*ss  ( 0 [,] +oo ) ) tsums  ( k  e.  A  |->  B ) )  e.  _V
32uniex 6479 . 2  |-  U. (
( RR*ss  ( 0 [,] +oo ) ) tsums  ( k  e.  A  |->  B ) )  e.  _V
41, 3eqeltri 2535 1  |- Σ* k  e.  A B  e.  _V
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758   _Vcvv 3071   U.cuni 4192    |-> cmpt 4451  (class class class)co 6193   0cc0 9386   +oocpnf 9519   [,]cicc 11407   ↾s cress 14286   RR*scxrs 14549   tsums ctsu 19821  Σ*cesum 26621
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4514  ax-nul 4522  ax-un 6475
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-v 3073  df-sbc 3288  df-dif 3432  df-un 3434  df-in 3436  df-ss 3443  df-nul 3739  df-sn 3979  df-pr 3981  df-uni 4193  df-iota 5482  df-fv 5527  df-ov 6196  df-esum 26622
This theorem is referenced by:  esumcvg  26673
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