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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
StepHypRef Expression
1 or32 527 . 2
2 sspss 3602 . . . 4
3 sspss 3602 . . . . 5
4 eqcom 2466 . . . . . 6
54orbi2i 519 . . . . 5
63, 5bitri 249 . . . 4
72, 6orbi12i 521 . . 3
8 orordir 531 . . 3
97, 8bitr4i 252 . 2
10 df-3or 974 . 2
111, 9, 103bitr4i 277 1
Colors of variables: wff setvar class
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
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