theorem
  M,v |= (p <=> q) => (p => q) & M |= (p <=> q) => (p => q)
proof
A1: now
    let v;
    M,v |= p <=> q implies M,v |= p => q by ZF_MODEL:15;
    hence M,v |= (p <=> q) => (p => q) by ZF_MODEL:18;
  end;
  hence M,v |= (p <=> q) => (p => q);
  let v;
  thus thesis by A1;
end;
