Intermediately characteristic of transfer-closed characteristic implies intermediately characteristic

Property-theoretic statement
If $$*$$ denotes the composition operator, we have:

Intermediately characteristic $$*$$ transfer-closed characteristic $$\le$$ Intermediately characteristic

Verbal statement
Any defining ingredient::intermediately characteristic subgroup of a defining ingredient::transfer-closed characteristic subgroup is intermediately characteristic.

Facts used

 * 1) uses::Characteristicity is transitive
 * 2) uses::Subhomomorphism relation between transfer-closure operator and intermediately operator over composition operator