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Theorem nssinpss 3729
 Description: Negation of subclass expressed in terms of intersection and proper subclass. (Contributed by NM, 30-Jun-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
nssinpss

Proof of Theorem nssinpss
StepHypRef Expression
1 inss1 3717 . . 3
21biantrur 506 . 2
3 df-ss 3489 . . 3
43necon3bbii 2718 . 2
5 df-pss 3491 . 2
62, 4, 53bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  /\wa 369  =/=wne 2652  i^icin 3474  C_wss 3475  C.wpss 3476 This theorem is referenced by:  fbfinnfr  20342  chrelat2i  27284 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-nfc 2607  df-ne 2654  df-v 3111  df-in 3482  df-ss 3489  df-pss 3491
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