This paper presents a generic algebraic proof of a recently published theorem [4], on the power conservative equivalent circuit for linear DC networks formed by time-invariant resistors and independent voltage and current sources. As the cited publication states, the internal losses of any network have two components: one variable and dependent on the internal resistances of the actual circuit and the power transferred to the pair of accessible terminals; and the other constant and dependent only on the internal voltage and current sources and the resistances of the actual network. It is also noted that the traditional ThÃ©venin and Norton equivalent circuits are particular cases of the proposed equivalent circuit.