Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfpss3 Unicode version

Theorem dfpss3 3589
 Description: Alternate definition of proper subclass. (Contributed by NM, 7-Feb-1996.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
dfpss3

Proof of Theorem dfpss3
StepHypRef Expression
1 dfpss2 3588 . 2
2 eqss 3518 . . . . 5
32baib 903 . . . 4
43notbid 294 . . 3
54pm5.32i 637 . 2
61, 5bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  /\wa 369  =wceq 1395  C_wss 3475  C.wpss 3476 This theorem is referenced by:  pssirr  3603  pssn2lp  3604  ssnpss  3606  nsspssun  3730  npss0  3865  pssdifcom1  3913  pssdifcom2  3914  php3  7723  fincssdom  8724  reclem2pr  9447  islbs3  17801  chpsscon3  26421  chpssati  27282  fundmpss  29196  ressval3d  32558  lpssat  34738  lssat  34741  dihglblem6  37067 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
 Copyright terms: Public domain W3C validator