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Theorem psstr 3607
 Description: Transitive law for proper subclass. Theorem 9 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
psstr

Proof of Theorem psstr
StepHypRef Expression
1 pssss 3598 . . 3
2 pssss 3598 . . 3
31, 2sylan9ss 3516 . 2
4 pssn2lp 3604 . . . 4
5 psseq1 3590 . . . . 5
65anbi1d 704 . . . 4
74, 6mtbiri 303 . . 3
87con2i 120 . 2
9 dfpss2 3588 . 2
103, 8, 9sylanbrc 664 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  C_wss 3475  C.wpss 3476 This theorem is referenced by:  sspsstr  3608  psssstr  3609  psstrd  3610  porpss  6584  inf3lem5  8070  ltsopr  9431 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ne 2654  df-in 3482  df-ss 3489  df-pss 3491
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