i came across a question with no proper explnation.
IF A is reduced to B and B belongs to NPC then we cant say anything about A since it can be as harder a NPH and as easier as P.
i know why it is as harder as NHP but i am not able to figure out about P class.

according to me if A > B(A polynomial time reducible to B) and B belongs to NPH then A is as easier as NPC and as harder as NPH.
A cannot belong to P since if A belongs to P then then in polynomial time i can solve P and in additional polynomial time i can reduce the results of A to suffice results of B.but as given B belongs to NPH and thus no polynomial time algorithm exists to solve B. which is contradiction to the assumption of A belongs to P.
can someone explain what mistake am i making?