theorem
  M,v |= p '&' q => q & M |= p '&' q => q
proof
  now
    let v;
    M,v |= p '&' q implies M,v |= q by ZF_MODEL:15;
    hence M,v |= p '&' q => q by ZF_MODEL:18;
  end;
  hence thesis;
end;
