The concept of A-subset is introduced in lattice implication algebras. Firstly, the properties of the A-subset are discussed when A is a general set of lattice implication algebras. Next, the properties of A-subset are investigated when the A is an LI-ideal of lattice implication algebras. We obtain some properties of A-subset and prove that B(A)(the A-subset of B) is an LI-ideal in lattice implication algebras. Finally, the properties of A-subset are investigated in lattice implication product algebras. We prove that the A-subset of is the product of A-subset of Bi (i = 1, 2, ⋯ , n) respectively .
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