According to the Arrhenius theory, the ionic conductivity of aqueous electrolytes is realized by the electrolyte ions. Water is considered to be a chemically inactive environmental media. Here, we succeeded in modeling the ionic dc conductivity and dielectric constant of aqueous HCl, NaOH and NaCl solutions without considering Na+ and Cl- ions. Instead, we assumed that i) water has a high concentration of the intrinsic H3O+ and OH- ions (much larger than it is implied by pH = 7), masked in the dc conductivity by the electrophoretic effect, i.e. by a strong ion-ion attraction, and ii) the chemical interaction between the electrolyte molecules and the water ions happens to break down the electrophoretic effect, thus "activating" the water ions for the dc conductivity. The hypothesis about the active role of water in the conductivity of electrolytes may look controversial, but nevertheless it consistently accounts for a set of basic empirical data and is therefore worth examining.