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Theorem pssn2lp 3277
 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 3262 . . . 4
21simprbi 450 . . 3
3 pssss 3271 . . 3
42, 3nsyl 113 . 2
5 imnan 411 . 2
64, 5mpbi 199 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358   wss 3152   wpss 3153 This theorem is referenced by:  psstr  3280  cvnsym  22870 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-ne 2448  df-in 3159  df-ss 3166  df-pss 3168
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