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Theorem modfsummodslem1 13606
Description: Lemma 1 for modfsummods 13607. (Contributed by Alexander van der Vekens, 1-Sep-2018.)
Assertion
Ref Expression
modfsummodslem1
Distinct variable groups:   ,   ,

Proof of Theorem modfsummodslem1
StepHypRef Expression
1 ssnid 4058 . . 3
2 elun2 3671 . . 3
31, 2ax-mp 5 . 2
4 rspcsbela 3853 . 2
53, 4mpan 670 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818  A.wral 2807  [_csb 3434  u.cun 3473  {csn 4029   cz 10889
This theorem is referenced by:  modfsummods  13607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030
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