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Theorem nsspssun 3730
 Description: Negation of subclass expressed in terms of proper subclass and union. (Contributed by NM, 15-Sep-2004.)
Assertion
Ref Expression
nsspssun

Proof of Theorem nsspssun
StepHypRef Expression
1 ssun2 3667 . . . 4
21biantrur 506 . . 3
3 ssid 3522 . . . . 5
43biantru 505 . . . 4
5 unss 3677 . . . 4
64, 5bitri 249 . . 3
72, 6xchnxbir 309 . 2
8 dfpss3 3589 . 2
97, 8bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  /\wa 369  u.cun 3473  C_wss 3475  C.wpss 3476 This theorem is referenced by:  disjpss  3877 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-or 370  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-un 3480  df-in 3482  df-ss 3489  df-pss 3491
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