The proof of addition formulas connecting Appell hypergeometric polynomials in two variables $F_2(a,-m+i,-i;p,q;x,y)$ and Lauricella polynomials $F_A(a,-m_1,\dots,-m_n;p_1,\dots,p_n;x_1,\dots,x_n)$ in $n$ variables with Gauss polynomial $F(a,-m;s;t)$ in one variable, is presented.