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

Step	Hyp	Ref	Expression
1		pssss 3598	. . 3
2		pssss 3598	. . 3
3	1, 2	sylan9ss 3516	. 2
4		pssn2lp 3604	. . . 4
5		psseq1 3590	. . . . 5
6	5	anbi1d 704	. . . 4
7	4, 6	mtbiri 303	. . 3
8	7	con2i 120	. 2
9		dfpss2 3588	. 2
10	3, 8, 9	sylanbrc 664	1

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