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Let ${\cal L}$ and ${\cal N}$ be propositional languages over Basic Propositional Calculus, and ${\cal M}={\cal L}\cap {\cal N}$. We prove two different but interrelated interpolation theorems. First, suppose that II is a sequent theory over ${\cal L}$, and $\Sigma \cup \{ C\Rightarrow C'\}$ is a set of sequents over ${\cal N}$, such that II, $\Sigma \vdash C \Rightarrow C'$. Then there is a sequent theory $\Phi$ over ${\cal M}$ such that $\Pi \vdash \Phi$ and $\Phi,\Sigma \vdash C\Rightarrow C'$. Second, let $A$ be a formula over ${\cal L}$,
and $C_1,C_2$ be formulas over ${\cal N}$, such that $A\wedge C_1\vdash C_2$. Then there exists a formula $B$ over ${\cal M}$
such that $A\vdash B$ and $B\wedge C_1\vdash C_2$.
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