But the "Mirror assembly" does not add the constrains,just the part. So you have to constrain the part anyway. In this case I would use "move with copy" and than fix it on the place. Seems as quicker way to me .
If mirror assembly command is not working for the condition you are trying, You can mirror body inside part, create the reference sets and use while adding it in assembly.
Is it the same part or a mirrored (symetrically opposite ) part?
Sometimes they are the same thing, other times not.
If its the same part number, I'd reposition and constrain it. If its a sym-opp part. makes a kinked mirrored body then position and constrain it.
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