The present law shall not apply to personnel who have similar rights (... ) , because they come from units under the Ministry of the Army.

Or

This law will not apply to personnel who have recognized similar rights,(...) as they come from units dependent on the Ministry of the Army.

I think fits very well.

In the example it's 'since they come from (or originate from) a particular establishment.
'It won't be by application of the present (current) law on personnel (staff-base or employees) who hold similar entitlements by the general legislation on subordinate (passive) social classes, since they come from (or originate from) units which depend on the ministry of the army (or armed forces).'

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Note added at 3 days 17 hrs (2021-02-21 21:40:41 GMT) Post-grading
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https://www.thefreedictionary.com/proceed
'Proceeding' is the present continuous part of the verb 'to proceed (from)', which is 'to initiate (from)' or 'to continue on from'.
In the explanation it can be read that they (those who are involved) come from a particular place or establishment. It explains that employment law is not applicable where employees are from army-based units.
('Procediendo es la parte continúa y presente del verbo 'proceder de' que es 'comenzar desde, 'originar de' o 'venir de'.
En la explicación se puede leer que ellos (los que están implicados vienen de un lugar o un establecimiento particular. Se explica que la ley de empleo no tiene que aplicarse donde los empleados son de unidades del ejército.)