let G be _Graph; :: thesis: ( ex v being Vertex of G st v is endvertex & G is regular implies G is 1 -regular )
assume A1: ( ex v being Vertex of G st v is endvertex & G is regular ) ; :: thesis: G is 1 -regular
then consider c being Cardinal such that
A2: G is c -regular ;
c = 1 by A1, A2, Th28;
hence G is 1 -regular by A2; :: thesis: verum