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"all being equal" is a correct and usable phrase in written English.
It is usually used after making a comparison, to indicate that all other things are the same in both cases. For example, "All being equal, I believe I will make the decision to go to the beach this weekend."
Exact(4)
They are sexual bullies themselves.Don't believe that stuff about them all being equal.
It seemed a comedically appealing idea: that in one sense a racist seeing the world as just four types of people is closer to the ultimate goal of us all being equal than a liberal who sees us as 195 distinct flavours.
All being equal, these disparate approaches produced truly riveting games that took full advantage of the features and processing capabilities of mobile devices.
All being equal, we prefer 'σ-finger', but we also understand the reviewers' points.
Similar(56)
We will finally all be equal in Turkey.
By hypothesis, they must all be equals.
Officially, all are equal.
On the turf, all are equal.
All are equal in prison uniform.
All were equal when it came to Bagshaw's typewriter.
Where all are equal in worth and value.
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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