Corollary

Let $d_1$ and $d_2$ be two $\varepsilon$-derivations from A to E of the same degree $\delta$. If $d_1$ and $d_2$ take the same values at each element of a generating system of the algebra A, then $d_1 = d_2$.

$d_1 - d_2$ is an $\varepsilon$-derivation of degree $\delta$, hence $\mathrm{Ker}(d_1 - d_2)$ is a subalgebra of A which contains a generating system of A and hence is equal to A.