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Theorem sstr 3008
 Description: Transitivity of subclasses. Theorem 6 of [Suppes] p. 23. (Contributed by NM, 5-Sep-2003.)
Assertion
Ref Expression
sstr ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)

Proof of Theorem sstr
StepHypRef Expression
1 sstr2 3007 . 2 (𝐴𝐵 → (𝐵𝐶𝐴𝐶))
21imp 122 1 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 102   ⊆ wss 2974 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987 This theorem is referenced by:  sstrd  3010  sylan9ss  3013  ssdifss  3103  uneqin  3222  ssindif0im  3310  undifss  3330  ssrnres  4793  relrelss  4874  fco  5087  fssres  5097  ssimaex  5266  tpostpos2  5914  smores  5941  iccsupr  9065
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