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Theorem en3lp 8033
 Description: No class has 3-cycle membership loops. This proof was automatically generated from the virtual deduction proof en3lpVD 32743 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 3789 . . . . 5
2 eleq2 2540 . . . . 5
31, 2mtbiri 303 . . . 4
4 tpid3g 4142 . . . 4
53, 4nsyl 121 . . 3
6 simp3 998 . . 3
75, 6nsyl 121 . 2
8 tpex 6583 . . . 4
98zfreg 8021 . . 3
10 en3lplem2 8032 . . . . . 6
1110com12 31 . . . . 5
1211necon2bd 2682 . . . 4
1312rexlimiv 2949 . . 3
149, 13syl 16 . 2
157, 14pm2.61ine 2780 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   w3a 973   wceq 1379   wcel 1767   wne 2662  wrex 2815   cin 3475  c0 3785  ctp 4031 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686  ax-un 6576  ax-reg 8018 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-nul 3786  df-sn 4028  df-pr 4030  df-tp 4032  df-uni 4246 This theorem is referenced by:  tratrb  32404  tratrbVD  32759  bj-inftyexpidisj  33703
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