theorem Th62:
  i <=> j in FI & j <=> k in FI implies i <=> k in FI
proof
  assume
A1: i <=> j in FI & j <=> k in FI;
  then j => i in FI & k => j in FI by Th8;
  then
A2: k => i in FI by Th41;
  i => j in FI & j => k in FI by A1,Th8;
  then i => k in FI by Th41;
  hence thesis by A2,Th8;
end;
