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

Step	Hyp	Ref	Expression
1		ssun2 3667	. . . 4
2	1	biantrur 506	. . 3
3		ssid 3522	. . . . 5
4	3	biantru 505	. . . 4
5		unss 3677	. . . 4
6	4, 5	bitri 249	. . 3
7	2, 6	xchnxbir 309	. 2
8		dfpss3 3589	. 2
9	7, 8	bitr4i 252	1

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