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The phrase "the reverse is not" is correct and can be used in written English
It is used to express the idea that the opposite of something is not true. For example, "Although I thought the test would be easy, the reverse is not true."
Exact(58)
But the reverse is not the case.
The reverse is not necessarily true.
The reverse is not always the case.
But, unfortunately for Obama, the reverse is not true.
Strangely, he said, the reverse is not true.
That the financial reality is the reverse is not a tellable truth.
All ore deposits are mineral deposits, but the reverse is not true.
Almost everyone who has sleep apnoea is a snorer, he said, although the reverse is not true.
Canadians grumble that, although Chinese firms can buy Canadian mining and hydrocarbons companies, the reverse is not true.
Similar(2)
Waterman [ 19] pointed out that "experiences of eudaimonia are always accompanied by experiences of hedonia, but…the reverse is not true" (p. 243).
For Graebner to look across a net and see Ashe and the reverse is not in itself unusual.
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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