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It is a natural counterpart of the category of finitely dominated integrable modules over the quantum classical (super) algebra of type $B_{m+n}$, $C_{m+n}$, $D_{m+n}$ or $B(0,m+n)$ from a viewpoint of super duality. We classify the irreducible modules in $\\mc{O}^{int}_q(m|n)$ and show that an irreducible module in $\\mc{O}^{int}_q(m|n)$ has a unique crystal base in case of type $B$ and $C$. 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