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Theorem nsspssun 3576
 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 3513 . . . 4
21biantrur 494 . . 3
3 ssid 3369 . . . . 5
43biantru 493 . . . 4
5 unss 3523 . . . 4
64, 5bitri 242 . . 3
72, 6xchnxbir 302 . 2
8 dfpss3 3435 . 2
97, 8bitr4i 245 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 178   wa 360   cun 3320   wss 3322   wpss 3323 This theorem is referenced by:  disjpss  3680 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338
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