reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;
reserve M for non empty set,
  m,m9 for Element of M,
  v,v9 for Function of VAR,M;
reserve i,j for Element of NAT;

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;
