reserve e for set;
reserve C,C1,C2,C3 for AltCatStr;
reserve C for non empty AltCatStr,
  o for Object of C;
reserve C for non empty transitive AltCatStr;

theorem Th33:
  for C being non empty AltCatStr, D being non empty SubCatStr of
C, o1,o2 being Object of C, p1,p2 being Object of D st o1 = p1 & o2 = p2 & <^p1
  ,p2^> <> {} for n being Morphism of p1,p2 holds n is Morphism of o1,o2
proof
  let C be non empty AltCatStr, D be non empty SubCatStr of C, o1,o2 be Object
  of C, p1,p2 be Object of D such that
A1: o1 = p1 & o2 = p2 & <^p1,p2^> <> {};
  let n be Morphism of p1,p2;
  n in <^p1,p2^> & <^p1,p2^> c= <^o1,o2^> by A1,Th31;
  hence thesis;
end;
