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Theorem sspsstri 3567
 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 529 . 2
2 sspss 3564 . . . 4
3 sspss 3564 . . . . 5
4 eqcom 2431 . . . . . 6
54orbi2i 521 . . . . 5
63, 5bitri 252 . . . 4
72, 6orbi12i 523 . . 3
8 orordir 533 . . 3
97, 8bitr4i 255 . 2
10 df-3or 983 . 2
111, 9, 103bitr4i 280 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wo 369   w3o 981   wceq 1437   wss 3436   wpss 3437 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-ne 2616  df-in 3443  df-ss 3450  df-pss 3452 This theorem is referenced by:  ordtri3or  5474  sorpss  6590  sorpssi  6591  funpsstri  30413
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