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Theorem sspsstr 3608
 Description: Transitive law for subclass and proper subclass. (Contributed by NM, 3-Apr-1996.)
Assertion
Ref Expression
sspsstr

Proof of Theorem sspsstr
StepHypRef Expression
1 sspss 3602 . 2
2 psstr 3607 . . . . 5
32ex 434 . . . 4
4 psseq1 3590 . . . . 5
54biimprd 223 . . . 4
63, 5jaoi 379 . . 3
76imp 429 . 2
81, 7sylanb 472 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  C_wss 3475  C.wpss 3476 This theorem is referenced by:  sspsstrd  3611  ordtr2  4927  php  7721  canthp1lem2  9052  suplem1pr  9451  fbfinnfr  20342  ppiltx  23451 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-or 370  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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