  We prove that if $M$ is a maximal $k$-edge-colorable subgraph of a multigraph
$G$ and if $F = \{v \in V(G) : d_M(v) \leq k-\mu(v)\}$, then $d_F(v) \leq
d_M(v)$ for all $v \in F$. (When $G$ is a simple graph, the set $F$ is just the
set of vertices having degree less than $k$ in $M$.) This implies Vizing's
Theorem as well as a special case of Tuza's Conjecture on packing and covering
of triangles. A more detailed version of our result also implies Vizing's
Adjacency Lemma for simple graphs.
