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Theorem sstr 3075
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 3074 . 2  |-  ( A 
C_  B  ->  ( B  C_  C  ->  A  C_  C ) )
21imp 123 1  |-  ( ( A  C_  B  /\  B  C_  C )  ->  A  C_  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    C_ wss 3041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-in 3047  df-ss 3054
This theorem is referenced by:  sstrd  3077  sylan9ss  3080  ssdifss  3176  uneqin  3297  ssindif0im  3392  undifss  3413  ssrnres  4951  relrelss  5035  fco  5258  fssres  5268  ssimaex  5450  tpostpos2  6130  smores  6157  pmss12g  6537  fidcenumlemr  6811  iccsupr  9717  fimaxq  10541  fsum2d  11172  fsumabs  11202  tgval  12145  tgvalex  12146  ssnei  12247  opnneiss  12254  restdis  12280  tgcnp  12305  blssexps  12525  blssex  12526  mopni3  12580  metss  12590  metcnp3  12607  tgioo  12642  cncfmptid  12679
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