Introduction to Linear Optimization: Driving the artificial variables out of the basis (case: no entries in the $j$-row are nonzero)
The Proof is on Theorem 2.5 of the section 2.3. If you consider the polyhedron with artificial variables and redundant equality constraints as P and original with no artificial variables and no redundant equality constraints as Q. As you may see, they assumes that the l(th) basic variable is an artificial variable, so remove it will not affect original polyhedron. On the Example 3.8, the last tableau with artificial variables shows a case where a row becomes zero. If this happens with non artificial variable we have a degeneracy case.