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Theorem nssinpss 3573
 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 3561 . . 3
21biantrur 493 . 2
3 df-ss 3334 . . 3
43necon3bbii 2632 . 2
5 df-pss 3336 . 2
62, 4, 53bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wa 359   wne 2599   cin 3319   wss 3320   wpss 3321 This theorem is referenced by:  fbfinnfr  17873  chrelat2i  23868 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-in 3327  df-ss 3334  df-pss 3336
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