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Theorem psstr 3049
 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 3039 . . 3
2 pssss 3039 . . 3
31, 2sylan9ss 2958 . 2
4 pssn2lp 3045 . . . 4
5 psseq1 3031 . . . . 5
65anbi1d 438 . . . 4
74, 6mtbiri 600 . . 3
87con2i 557 . 2
9 dfpss2 3029 . 2
103, 8, 9sylanbrc 394 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wceq 1243   wss 2917   wpss 2918 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ne 2206  df-in 2924  df-ss 2931  df-pss 2933 This theorem is referenced by:  psstrd  3052
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