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Theorem pssn2lp 3434
 Description: Proper subclass has no 2-cycle loops. Compare Theorem 8 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
pssn2lp

Proof of Theorem pssn2lp
StepHypRef Expression
1 dfpss3 3419 . . . 4
21simprbi 452 . . 3
3 pssss 3428 . . 3
42, 3nsyl 116 . 2
5 imnan 413 . 2
64, 5mpbi 201 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   wss 3306   wpss 3307 This theorem is referenced by:  psstr  3437  cvnsym  23824 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-ne 2607  df-in 3313  df-ss 3320  df-pss 3322
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