Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sspsstr Structured version   Unicode version

Theorem sspsstr 3570
 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 3564 . 2
2 psstr 3569 . . . . 5
32ex 434 . . . 4
4 psseq1 3552 . . . . 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 1370   wss 3437   wpss 3438 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-ne 2650  df-in 3444  df-ss 3451  df-pss 3453 This theorem is referenced by:  sspsstrd  3573  ordtr2  4872  php  7606  canthp1lem2  8932  suplem1pr  9333  fbfinnfr  19547  ppiltx  22649
 Copyright terms: Public domain W3C validator