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Theorem en2lp 7563
 Description: No class has 2-cycle membership loops. Theorem 7X(b) of [Enderton] p. 206. (Contributed by NM, 16-Oct-1996.) (Revised by Mario Carneiro, 25-Jun-2015.)
Assertion
Ref Expression
en2lp

Proof of Theorem en2lp
StepHypRef Expression
1 zfregfr 7562 . . 3
2 efrn2lp 4556 . . 3
31, 2mpan 652 . 2
4 elex 2956 . . . 4
5 elex 2956 . . . 4
64, 5anim12i 550 . . 3
76con3i 129 . 2
83, 7pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 359   wcel 1725  cvv 2948   cep 4484   wfr 4530 This theorem is referenced by:  preleq  7564  suc11reg  7566  axunndlem1  8462  axacndlem5  8478  tratrb  28557  tratrbVD  28910 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-reg 7552 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-eprel 4486  df-fr 4533
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