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The phrase "without equality with" is correct and usable in written English.
It can be used in contexts discussing relationships, comparisons, or conditions where equality is not present or applicable. Example: "The two parties entered the agreement without equality with respect to their bargaining power."
Exact(1)
When will she realise that all talk of democracy is bullshit without equality with men?
Similar(59)
"Thereby associating the name of he who wrote 'there cannot be perfect and complete political equality without economic equality' with a powerful symbol of luxury and inequality," said Montanari.
The fully active suspension system provides much better body isolation than the other types with or without equality constraint.
But without equality and fraternity, they are unable to share wealth with the vast masses of people still excluded from the fruits of civilization.
We saw earlier the idea that set theory is the theory of one extensional binary relation (with equality of course: extensionality cannot be defined in a language without equality).
There is no freedom without equality".
–Can you have peace without equality?
Cameron said: "You can't have true opportunity without equality.
You can be free, but without equality, you can't expand — you can't grow".
Two results are obtained in terms of strict linear matrix inequalities (LMIs) without equality constraint.
It's advantage without equality.
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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