Vertices of degree 6 in a 6-contraction critical graph

An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be a k-contraction critical graph. We prove that every 6-contraction critical graph of order n, has at least n/7, vertices of degree 6.