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The phrase "back up the" is correct and usable in written English.
It can be used when referring to supporting or reinforcing something, such as a statement, argument, or data.
Example: "Please back up the claims you made in your presentation with relevant data."
Alternatives: "support the" or "reinforce the".
Exact(60)
"Back up!" the truck-driver snarled.
"Go back up the mountain," he said.
The Times seems to back up the linguist's assessment.
Offended, I turn back up the damp steps.
In truth, there's a lot to back up the score.
Last ,empirical results to back up the claims are presented.
The array was designed to back up the existing hardware instrumentation in the process unit.
At present, there is no empirical evidence to back up the fear of false reassurance.
"I think the science they used to back up the report is very mainstream," she adds.
The resulting prediction error is then passed back up the hierarchy, to optimise high-level representations.
Which items are required to back up the claims of a journal publication?
More suggestions(16)
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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