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Theorem sstri 3281
 Description: Subclass transitivity inference. (Contributed by NM, 5-May-2000.)
Hypotheses
Ref Expression
sstri.1 A B
sstri.2 B C
Assertion
Ref Expression
sstri A C

Proof of Theorem sstri
StepHypRef Expression
1 sstri.1 . 2 A B
2 sstri.2 . 2 B C
3 sstr2 3279 . 2 (A B → (B CA C))
41, 2, 3mp2 17 1 A C
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  snsstp1  3858  snsstp2  3859  uniintsn  3963  inxpk  4277  dfidk2  4313  ssrnres  5059  fvfullfunlem3  5863  sbthlem1  6203  spacssnc  6284
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