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Theorem esumeq2 28809
 Description: Equality theorem for extended sum. (Contributed by Thierry Arnoux, 24-Dec-2016.)
Assertion
Ref Expression
esumeq2 Σ* Σ*
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem esumeq2
StepHypRef Expression
1 eqid 2428 . . . . 5
2 mpteq12 4446 . . . . 5
31, 2mpan 674 . . . 4
43oveq2d 6265 . . 3 s tsums s tsums
54unieqd 4172 . 2 s tsums s tsums
6 df-esum 28801 . 2 Σ* s tsums
7 df-esum 28801 . 2 Σ* s tsums
85, 6, 73eqtr4g 2487 1 Σ* Σ*
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1437  wral 2714  cuni 4162   cmpt 4425  (class class class)co 6249  cc0 9490   cpnf 9623  cicc 11589   ↾s cress 15065  cxrs 15341   tsums ctsu 21082  Σ*cesum 28800 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719  df-rex 2720  df-rab 2723  df-v 3024  df-dif 3382  df-un 3384  df-in 3386  df-ss 3393  df-nul 3705  df-if 3855  df-sn 3942  df-pr 3944  df-op 3948  df-uni 4163  df-br 4367  df-opab 4426  df-mpt 4427  df-iota 5508  df-fv 5552  df-ov 6252  df-esum 28801 This theorem is referenced by: (None)
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