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The paper presents a flexible and efficient approach to evaluating implications as well as deriving indirect implications in logic circuits. Evaluation and derivation of implications are essential in ATPG, equivalence checking, and netlist optimization. Contrary to other methods, the approach is based on a graph model of a circuit's clause description called implication graph. It combines both the flexibility of SAT-based techniques and high efficiency of structure based methods. As the proposed algorithms operate only on the implication graph, they are independent of the chosen logic. Evaluation of implications and computation of indirect implications are performed by simple and efficient graph algorithms. Experimental results for various applications relying on implication demonstrate the effectiveness of the approach.