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
  H is disjunctive implies (M,v |= H iff M,v |= the_left_argument_of H
  or M,v |= the_right_argument_of H)
proof
  assume H is disjunctive;
  then H = (the_left_argument_of H) 'or' (the_right_argument_of H) by
ZF_LANG:41;
  hence thesis by ZF_MODEL:17;
end;
