Theorem sspsstri 3605

Description: Two ways of stating trichotomy with respect to inclusion. (Contributed by NM, 12-Aug-2004.)

Assertion

Ref	Expression
sspsstri

Proof of Theorem sspsstri

Step	Hyp	Ref	Expression
1		or32 527	. 2
2		sspss 3602	. . . 4
3		sspss 3602	. . . . 5
4		eqcom 2466	. . . . . 6
5	4	orbi2i 519	. . . . 5
6	3, 5	bitri 249	. . . 4
7	2, 6	orbi12i 521	. . 3
8		orordir 531	. . 3
9	7, 8	bitr4i 252	. 2
10		df-3or 974	. 2
11	1, 9, 10	3bitr4i 277	1

Syntax hints:  <->wb 184  \/wo 368  \/w3o 972  =wceq 1395  C_wss 3475  C.wpss 3476

This theorem is referenced by:  ordtri3or  4915  sorpss  6585  sorpssi  6586  funpsstri  29195

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-3or 974  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ne 2654  df-in 3482  df-ss 3489  df-pss 3491