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Theorem sstr 3280
 Description: Transitivity of subclasses. Theorem 6 of [Suppes] p. 23. (Contributed by NM, 5-Sep-2003.)
Assertion
Ref Expression
sstr ((A B B C) → A C)

Proof of Theorem sstr
StepHypRef Expression
1 sstr2 3279 . 2 (A B → (B CA C))
21imp 418 1 ((A B B C) → A C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  sstrd  3282  sylan9ss  3285  ssdifss  3397  uneqin  3506  sspw1  4335  ssrnres  5059  fco  5231  fssres  5238  ssetpov  5944  sbthlem1  6203
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