Abstract: The reference [4] proved the consistency of S₁ and S₂ among Lewis’ five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S₃, S₄ and S₅ in Lewis’ five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S₃ and P₃, S₄ and P₄; (2) the modal systems P₃ and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in V^B. Hence, the paper proves: (a) ‖As₃1‖ = 1; (b) ‖AS₄1‖ = 1; (c) ‖AS₅l‖ = 1 in the model <V^B, R, ‖ ‖>(where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model V^B of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis’ the strict implication system S³, S⁴ and S^5. 

Key words: the , strict implication , system;Boolean-valued model;Boolean value