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 Thévenin and Norton equivalent circuits are particular cases of the proposed equivalent circuit.