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Theorem en3lp 8067
 Description: No class has 3-cycle membership loops. This proof was automatically generated from the virtual deduction proof en3lpVD 37151 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 3701 . . . . 5
2 eleq2 2489 . . . . 5
31, 2mtbiri 304 . . . 4
4 tpid3g 4051 . . . 4
53, 4nsyl 124 . . 3
65intn3an3d 1376 . 2
7 tpex 6541 . . . 4
87zfreg 8056 . . 3
9 en3lplem2 8066 . . . . . 6
109com12 32 . . . . 5
1110necon2bd 2611 . . . 4
1211rexlimiv 2844 . . 3
138, 12syl 17 . 2
146, 13pm2.61ine 2678 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   w3a 982   wceq 1437   wcel 1872   wne 2593  wrex 2709   cin 3371  c0 3697  ctp 3938 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2402  ax-sep 4482  ax-nul 4491  ax-pr 4596  ax-un 6534  ax-reg 8053 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2552  df-ne 2595  df-ral 2713  df-rex 2714  df-v 3018  df-dif 3375  df-un 3377  df-in 3379  df-nul 3698  df-sn 3935  df-pr 3937  df-tp 3939  df-uni 4156 This theorem is referenced by:  bj-inftyexpidisj  31553  tratrb  36804  tratrbVD  37168
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