"carries the implication of" is a correct and usable phrase in written English.
You can use it to refer to something that is suggested or implied but not directly stated. For example, "His silence carries the implication of guilt."
The term carries the implication of the low estate into which the poet has fallen from his ancient position as seer and prophet.
"Arabic-language instruction is inevitably laden with Pan-Arabist and Islamist baggage," he wrote, referring to the school as a madrassa, which means school in Arabic but, in the West, carries the implication of Islamic teaching.
And yet I love most of these bands, and I think I love noise: it carries the implication of energy and unpredictability, and describes something outside or beyond notes.
This biased view of 17th-century art styles was held with few modifications by critics from Johann Winckelmann to John Ruskin and Jacob Burckhardt, and until the late 19th century the term always carried the implication of odd, grotesque, exaggerated, and overdecorated.
However, low values sometimes occurred in woods or near trees, so that rarity of tree-associated insects in archaeological deposits does not always carry the implication of a treeless environment.
Tim Malloy, assistant director of the Quinnipiac poll, said that to him it implied people were interpreting "gun laws" as generic safeguards such as background checks, while "gun control" was a more absolute term which carried the implication of guns being fully taken away.
"The papers use emotive language to threaten a future of financial meltdown and they carry the implication of the destruction of the game should a newco not be entered in the First Division.
Ownership carries the implication that one is of lesser means, a good thing in a city where having money draws attention of the wrong kind.
This carried the implication that when an odd number of atoms appeared in a published organic formula, the analysis was inaccurate.
The concept of periodic random dominance as an aspect of landform evolution carries with it the implication of polygenetic landforms and landscapes where geomorphic system dominance fails to develop.
