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