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Theorem en3lp 8054
Description: No class has 3-cycle membership loops. This proof was automatically generated from the virtual deduction proof en3lpVD 33645 using a translation program. (Contributed by Alan Sare, 24-Oct-2011.)
Assertion
Ref Expression
en3lp

Proof of Theorem en3lp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 noel 3788 . . . . 5
2 eleq2 2530 . . . . 5
31, 2mtbiri 303 . . . 4
4 tpid3g 4145 . . . 4
53, 4nsyl 121 . . 3
65intn3an3d 1340 . 2
7 tpex 6599 . . . 4
87zfreg 8042 . . 3
9 en3lplem2 8053 . . . . . 6
109com12 31 . . . . 5
1110necon2bd 2672 . . . 4
1211rexlimiv 2943 . . 3
138, 12syl 16 . 2
146, 13pm2.61ine 2770 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  /\w3a 973  =wceq 1395  e.wcel 1818  =/=wne 2652  E.wrex 2808  i^icin 3474   c0 3784  {ctp 4033
This theorem is referenced by:  tratrb  33307  tratrbVD  33661  bj-inftyexpidisj  34613
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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592  ax-reg 8039
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-nul 3785  df-sn 4030  df-pr 4032  df-tp 4034  df-uni 4250
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