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The phrase "everything else being equal" is a perfectly correct and usable phrase in written English.
You can use it when you want to compare two or more similar things or ideas, as long as the comparison is assuming that all other factors are the same. For example, "It's cheaper to stay at home for vacation, everything else being equal."
Exact(55)
"Everything else being equal, the fewer miles we drive, the fewer deer we hit".
She added, "I'd prefer, everything else being equal, not to be the punching bag for anyone".
I'm willing to concede that, everything else being equal, a three-fin thruster turns better than a single-fin does.
It found that, everything else being equal, people who used less health care were no less healthy than those who used more.
Everything else being equal, Mackay and Hunter were master footballers, the tragedy of Hunter's career being the fact that he was born around the time of Bobby Moore.
Everything else being equal -- not that everything ever is -- shortstops and catchers receive extra consideration for the difficulty of their positions.
Similar(5)
"If everything else is equal, the guy with the most money wins".
And it's clear that if everything else is equal, a smaller class is better than a larger class.
Teams like to say they go for best available player, and that's true in a lot of cases, assuming everything else is equal.
If the Braves maintain their mastery over the Mets next season, the extra games they play could make a huge difference in the distance between them, given that everything else is equal.
Let these generous sentiments be supposed ever so weak; let them be insufficient to move even a hand or finger of our body; they must still direct the determinations of our mind, and where everything else is equal, produce a cool preference of what is useful and serviceable to mankind, above what is pernicious and dangerous.
More suggestions(3)
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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