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The phrase "a third condition" is correct and usable in written English.
You can use it when referring to an additional requirement or stipulation in a list of conditions or criteria.
Example: "In addition to the first two conditions, we must also consider a third condition that affects the overall outcome."
Alternatives: "an additional condition" or "a further condition".
Exact(44)
In the Sydney Swirl burner data, the two-condition conditional averages exhibit modest gradients in space which are attributed to heat transfer with the bluff body in the flow; when a third condition is added – based on the total enthalpy – the spatial gradients in the conditional average of temperature a dramatically reduced.
Following treatment, a third condition was conducted that reduced the total number of reinforcers available per session to baseline levels.
He then tested the fish's movements in light and dark conditions, and in a third condition where he replaced the water with tin foil.
Oysters display a third condition; young oysters have a tendency toward maleness, but, if water temperature or food availability is altered, some individuals develop into females.
A third condition, Hallerman-Streiff-François syndrome, is characterized by the presence of progeria in combination with dwarfism and other features of abnormal growth.
A third condition, which is connected to the first two, is the formal establishment of laws and policies that restrict rights, usually on the grounds of preventing terrorism and protecting national economic interests.
Similar(16)
At this point, a second condition was introduced.
A second condition takes account of the cloud's thickness.
A first condition is that the debates be focused on specific points of major disagreement.
A second condition consisting of the same ACT condition with an added emphasis on values and committed action.
In a second condition, participants maintained the identical premises of these problems in working memory without making inferences.
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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