Graph labeling is the assignment of integers to edges or vertices or both depending on some factors which is consequential in the field of graph theory. In this paper, anti-magic graph labeling of two graphs, middle graph and total graph of path graph have been mainly focused. Modified proofs of theorems on anti-magic graph labeling have been introduced here. Both of the theorems are applicable for strong anti-magic graph. The correctness of the proofs has been demonstrated through various examples.