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Theorem sspsstri 3451
 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 515 . 2
2 sspss 3448 . . . 4
3 sspss 3448 . . . . 5
4 eqcom 2440 . . . . . 6
54orbi2i 507 . . . . 5
63, 5bitri 242 . . . 4
72, 6orbi12i 509 . . 3
8 orordir 519 . . 3
97, 8bitr4i 245 . 2
10 df-3or 938 . 2
111, 9, 103bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wo 359   w3o 936   wceq 1653   wss 3322   wpss 3323 This theorem is referenced by:  ordtri3or  4615  sorpss  6529  sorpssi  6530  funpsstri  25391 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ne 2603  df-in 3329  df-ss 3336  df-pss 3338
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