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We study the isomorphic implication problem for Boolean constraints. We show that this is a natural analog of the subgraph isomorphism problem. We prove that, depending on the set of constraints, this problem is in P, NP-complete, or NP-hard, coNP-hard, and in ${\rm P^{NP}_{||}}$. We show how to extend the NP-hardness and coNP-hardness to ${\rm P^{NP}_{||}}$-hardness for some cases, and conjecture that this can be done in all cases.