Transfer condition operator preserves intersection-closedness

Statement
Suppose $$T$$ is the fact about::transfer condition operator. Then:


 * If $$p$$ is a fact about::finite-intersection-closed subgroup property, so is $$T(p)$$.
 * If $$p$$ is an fact about::intersection-closed subgroup property, so is $$T(p)$$.

Related facts

 * Subhomomorphism relation between transfer condition operator and intersection operator
 * Intersection-closure operator preserves transfer condition