theorem Th102:
  M,v |= p => q & M,v |= q => r implies M,v |= p => r
proof
  assume that
A1: M,v |= p => q and
A2: M,v |= q => r;
  M |= (p => q) => ((q => r) => (p => r)) by Th101;
  then M,v |= (p => q) => ((q => r) => (p => r));
  then M,v |= (q => r) => (p => r) by A1,ZF_MODEL:18;
  hence thesis by A2,ZF_MODEL:18;
end;
