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Theorem nfesum1 26632
Description: Bound-variable hypothesis builder for extended sum. (Contributed by Thierry Arnoux, 19-Oct-2017.)
Hypothesis
Ref Expression
nfesum1.1  |-  F/_ k A
Assertion
Ref Expression
nfesum1  |-  F/_ kΣ* k  e.  A B

Proof of Theorem nfesum1
StepHypRef Expression
1 df-esum 26620 . 2  |- Σ* k  e.  A B  =  U. (
( RR*ss  ( 0 [,] +oo ) ) tsums  ( k  e.  A  |->  B ) )
2 nfcv 2613 . . . 4  |-  F/_ k
( RR*ss  ( 0 [,] +oo ) )
3 nfcv 2613 . . . 4  |-  F/_ k tsums
4 nfmpt1 4481 . . . 4  |-  F/_ k
( k  e.  A  |->  B )
52, 3, 4nfov 6215 . . 3  |-  F/_ k
( ( RR*ss  (
0 [,] +oo )
) tsums  ( k  e.  A  |->  B ) )
65nfuni 4197 . 2  |-  F/_ k U. ( ( RR*ss  (
0 [,] +oo )
) tsums  ( k  e.  A  |->  B ) )
71, 6nfcxfr 2611 1  |-  F/_ kΣ* k  e.  A B
Colors of variables: wff setvar class
Syntax hints:   F/_wnfc 2599   U.cuni 4191    |-> cmpt 4450  (class class class)co 6192   0cc0 9385   +oocpnf 9518   [,]cicc 11406   ↾s cress 14279   RR*scxrs 14542   tsums ctsu 19814  Σ*cesum 26619
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-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3072  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-nul 3738  df-if 3892  df-sn 3978  df-pr 3980  df-op 3984  df-uni 4192  df-br 4393  df-opab 4451  df-mpt 4452  df-iota 5481  df-fv 5526  df-ov 6195  df-esum 26620
This theorem is referenced by:  esumfsup  26655  oms0  26846
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