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Theorem nsspssun 2231

Description: Negation of subclass expressed in terms of proper subclass and union.

Assertion

Ref	Expression
nsspssun

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Proof of Theorem nsspssun

Step	Hyp	Ref	Expression
1		ssun2 2184	. . 3
2	1	biantrur 723	. 2
3		ssid 2070	. . . . 5
4	3	biantru 722	. . . 4
5		unss 2194	. . . 4
6	4, 5	bitr 173	. . 3
7	6	negbii 187	. 2
8		dfpss3 2124	. 2
9	2, 7, 8	3bitr4 183	1

Colors of variables: wff set class

Syntax hints:   wn 2   wb 146   wa 223   cun 2035   wss 2037   wpss 2038

This theorem is referenced by:  disjpss 2309

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-v 1803  df-un 2040  df-in 2041  df-ss 2043  df-pss 2045

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