The simple substitution property provides a systematic and easy method for proving a theorem by an axiomatic way. The notion of the property was introduced in Hosoi [4] but without a definite name and he showed three examples of the axioms with the property. Later, the property was given it's name as above in Sasaki [7].Our main result here is that the necessary and sufficient condition for a logicL on a finite slice to have the simple substitution property is thatL (...) is finite. Here the necessity part is essentially new, for the sufficiency part has been proved in Hosoi and Sasaki [5]. Also the proof of sufficiency part is improved here. (shrink)