Theorem sstr 1511

Description: Transitivity of subclasses. Theorem 6 of [Suppes] p. 23.

Assertion

Ref	Expression
sstr	|- ((A (_ B /\ B (_ C) -> A (_ C)

Proof of Theorem sstr

Step	Hyp	Ref	Expression
1		sstr2 1510	. 2 |- (A (_ B -> (B (_ C -> A (_ C))
2	1	imp 277	1 |- ((A (_ B /\ B (_ C) -> A (_ C)

Syntax hints:   -> wi 2   /\ wa 196   (_ wss 1487

This theorem is referenced by:  sstrd 1513  fssres 2764  unblem1 3431  unblem2 3432  unblem3 3433  unblem4 3434  isfinite2 3437  fodom 3613  uzwo 4605  uzwo2 4606  infxpidmlem11 4943  chsspwh 5154  shsupunss 5316  chsupunss 5317  spanss 5319  shlub 5347  shslub 5359  shmod 5364  atcvatlem 5770  mdsymlem5 5780

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-in 1491  df-ss 1492

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