The fundamental property of electrolytic systems, involved with linear combination 2∙f (O) – f (H) of elemental balances: f (H) for H and f (O) for O, is presented in terms of the Generalized Approach to Electrolytic Systems (GATES). The balance 2∙f (O) – f (H) is: (a) linearly dependent on charge balance (ChB) and other elemental and/or core balances f (Yj) (Yj ≠ H, O) related to a non-redox system, or (b) linearly independent on these balances, when related to a redox system. This dependency/independency property of 2∙f (O) – f (H) is the general criterion distinguishing between non-redox and redox systems, of any degree of complexity. It clearly explains why the balances: f (H) and f (O and then 2∙f (O) – f (H) are not formulated for non-redox systems. For a redox system, 2∙f (O) – f (H) is the primary form of Generalized Electron Balance (GEB), formulated according to Approach II to GEB and considered as the fundamental/indispensable equation needed for resolution of electrolytic redox systems according to GATES/GEB principles. These general properties are proved in the related examples and extended on other systems. The paper provides simple regularities that enable to check the dependency/independency criterion and formulate the GEB for redox systems.