Abstract:Applying T-norm to fuzzy congruences in lattice implication algebras, the notions of T-fuzzy congruences of lattices implication algebras is introduced. Through the probe into the corresponding properties and some equivalent characterizations, a conclusion is reached that that the set TFF(L) of all T-fuzzy filters is isomorphic to the set TFC(L) of all T-fuzzy congruences; and in the end, the quotient lattices implication and homomorphism theorem are thus obtained.