In this paper, we first transform a set of moment conditions into a set of transformed moment conditions, based on which the efficient partial generalized method of moments estimation for part of a parameter vector is defined. Given the set of transformed moment conditions, we then show that the conditions for partial redundancy of an additional set of moment conditions given an original set of moment conditions simply become the conditions for full redundancy of the second subset of transformed moment conditions given the first subset of transformed moment conditions. Thus the transformed moment conditions proposed in this paper unify partial redundancy of moment conditions with full redundancy of moment conditions. Using transformed moment conditions, we then straightforwardly derive necessary and sufficient conditions for partial redundancy of one or two subset(s) of moment conditions given the other when the large set of moment conditions consists of three subsets of moment conditions. The paper also provides several easily checkable sufficient conditions for partial redundancy of one set of moment conditions given other sets of moment conditions.