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When cathode has a higher value than anode, it makes the E positive since E=Ecathode=Eanode. We now know that the reaction favors the products because G=-nFE. If E is positive, G is negative and therefore, the reaction will spontaneously form products.
Another way you can think of it is that E represents standard Reduction potential, not oxidation potential, so you want E for the cathode to be big (since reduction occurs at the cathode) and E for the anode to be small, preferably negative, (since oxidation occurs at the anode). If this is true then E of the total cell will be positive, and G will be negative, which means it is spontaneous.
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