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The phrase "a negative implication" is correct and usable in written English.
It can be used when discussing the potential adverse consequences or meanings that may arise from a statement or action.
Example: "The new policy has a negative implication for employee morale, as it may lead to increased stress and dissatisfaction."
Alternatives: "a detrimental effect" or "a harmful connotation."
Exact(12)
"It will have a negative implication to those sitting in middle America".
However, it has a negative implication in proximity effect correction, i.e. lengthening correction time.
"So to admit that you don't understand something, particularly in a business context, can have a negative implication".
The Supreme Court has long interpreted this affirmative grant of power as containing a negative implication: the states themselves may not regulate interstate commerce.
[T]he search for a negative implication from mandatory language in prisoner regulations has strayed from the real concerns undergirding the liberty protected by the Due Process Clause.
But it also carries a negative implication: plenty of Mr Kerry's own side now think he is going to lose.This crisis of confidence seems to have infected the Kerry campaign.
Similar(48)
This is necessary to avoid any negative implication on inflation.
"We divest any negative implication from the word and toss it around with love".
Focusing on the anatomy and physiology of the pain transmission system, Valerie Hardcastle (1997) urges a similar negative implication for a popular methodological assumption.
Allodynia occurring during migraine attack and persistent pericranial tenderness in migraine and tension type headache are symptoms of central sensitization [15, 16], which may be aggravated by sleep disturbances and/or exert a negative impact on sleep in a mutual negative implication.
This was done because of habitat fragmentation can have a bigger negative implication on ecological connectivity and well-being of residing fauna and flora (Fahrig 2003).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com