Mathbox for Thierry Arnoux < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ballotlemelo Structured version   Unicode version

Theorem ballotlemelo 24745
 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 5728 . . . 4
21eqeq1d 2444 . . 3
3 ballotth.o . . . 4
4 fveq2 5728 . . . . . 6
54eqeq1d 2444 . . . . 5
65cbvrabv 2955 . . . 4
73, 6eqtri 2456 . . 3
82, 7elrab2 3094 . 2
9 ovex 6106 . . . 4
109elpw2 4364 . . 3
1110anbi1i 677 . 2
128, 11bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  crab 2709   wss 3320  cpw 3799  cfv 5454  (class class class)co 6081  c1 8991   caddc 8993  cn 10000  cfz 11043  chash 11618 This theorem is referenced by:  ballotlemscr  24776  ballotlemro  24780  ballotlemfg  24783  ballotlemfrc  24784  ballotlemfrceq  24786  ballotlemrinv0  24790 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084
 Copyright terms: Public domain W3C validator