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Theorem ballotlemelo 23046
 Description: Elementhood in . (Contributed by Thierry Arnoux, 17-Apr-2017.)
Hypotheses
Ref Expression
ballotth.m
ballotth.n
ballotth.o
Assertion
Ref Expression
ballotlemelo
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ballotlemelo
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5525 . . . 4
21eqeq1d 2291 . . 3
3 ballotth.o . . . 4
4 nfcv 2419 . . . . 5
5 nfcv 2419 . . . . 5
6 nfv 1605 . . . . 5
7 nfv 1605 . . . . 5
8 fveq2 5525 . . . . . 6
98eqeq1d 2291 . . . . 5
104, 5, 6, 7, 9cbvrab 2786 . . . 4
113, 10eqtri 2303 . . 3
122, 11elrab2 2925 . 2
13 elex 2796 . . . 4
14 ovex 5883 . . . . 5
1514ssex 4158 . . . 4
16 elpwg 3632 . . . 4
1713, 15, 16pm5.21nii 342 . . 3
1817anbi1i 676 . 2
1912, 18bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358   wceq 1623   wcel 1684  crab 2547  cvv 2788   wss 3152  cpw 3625  cfv 5255  (class class class)co 5858  c1 8738   caddc 8740  cn 9746  cfz 10782  chash 11337 This theorem is referenced by:  ballotlemscr  23077  ballotlemro  23081  ballotlemfg  23084  ballotlemfrc  23085  ballotlemfrceq  23087  ballotlemrinv0  23091 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-pw 3627  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861
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