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Theorem sspss 3368
 Description: Subclass in terms of proper subclass. (Contributed by NM, 25-Feb-1996.)
Assertion
Ref Expression
sspss

Proof of Theorem sspss
StepHypRef Expression
1 dfpss2 3354 . . . . 5
21simplbi2 608 . . . 4
32con1d 116 . . 3
43orrd 367 . 2
5 pssss 3364 . . 3
6 eqimss 3323 . . 3
75, 6jaoi 368 . 2
84, 7impbii 180 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 176   wo 357   wceq 1642   wss 3257   wpss 3258 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  sspsstri  3371  sspsstr  3374  psssstr  3375  ssfin  4470
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