New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  dfpss3 Unicode version

Theorem dfpss3 3355
 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 3354 . 2
2 eqss 3287 . . . . 5
32baib 871 . . . 4
43notbid 285 . . 3
54pm5.32i 618 . 2
61, 5bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 176   wa 358   wceq 1642   wss 3257   wpss 3258 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pss 3261 This theorem is referenced by:  pssirr  3369  pssn2lp  3370  ssnpss  3372  nsspssun  3488  npss0  3589  pssdifcom1  3635  pssdifcom2  3636  dfpss4  3888
 Copyright terms: Public domain W3C validator