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Theorem psstr 3523
 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 3514 . . 3
2 pssss 3514 . . 3
31, 2sylan9ss 3431 . 2
4 pssn2lp 3520 . . . 4
5 psseq1 3506 . . . . 5
65anbi1d 719 . . . 4
74, 6mtbiri 310 . . 3
87con2i 124 . 2
9 dfpss2 3504 . 2
103, 8, 9sylanbrc 677 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 376   wceq 1452   wss 3390   wpss 3391 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-ne 2643  df-in 3397  df-ss 3404  df-pss 3406 This theorem is referenced by:  sspsstr  3524  psssstr  3525  psstrd  3526  porpss  6594  inf3lem5  8155  ltsopr  9475
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