We study the learning models defined by Angluin et al. (1997): learning with equivalence and limited membership queries and learning with equivalence and malicious membership queries. We show that if a class of concepts that is closed under projection is learnable in polynomial time using equivalence and (standard) membership queries then it is learnable in polynomial time in the above models. This closes the open problems by Angluin et al. (1997). Our algorithm can also handle errors in the equivalence queries.