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Theorem sstr 3016
Description: Transitivity of subclasses. Theorem 6 of [Suppes] p. 23. (Contributed by NM, 5-Sep-2003.)
Assertion
Ref Expression
sstr  |-  ( ( A  C_  B  /\  B  C_  C )  ->  A  C_  C )

Proof of Theorem sstr
StepHypRef Expression
1 sstr2 3015 . 2  |-  ( A 
C_  B  ->  ( B  C_  C  ->  A  C_  C ) )
21imp 122 1  |-  ( ( A  C_  B  /\  B  C_  C )  ->  A  C_  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    C_ wss 2982
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 2065
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-in 2988  df-ss 2995
This theorem is referenced by:  sstrd  3018  sylan9ss  3021  ssdifss  3112  uneqin  3231  ssindif0im  3319  undifss  3339  ssrnres  4813  relrelss  4894  fco  5107  fssres  5117  ssimaex  5286  tpostpos2  5934  smores  5961  iccsupr  9117
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