Let $G = (V,E)$ be an $n$-vertex graph and let $c: E \to \mathbb{N}$ be a coloring of its edges. Let $d^c(v)$ be the number of distinct colors on the edges at $v \in V$ and let $δ^c(G) = \min_{v \in V} \{ d^{c}(v) \}$. H. Li proved that $δ^c(G) > n/2$ guarantees a rainbow triangle in $G$. We give extensions of Li's result to cliques $K_r$ for $r \ge 4$.