An important principle would be:
Would the installation of a washer or a dryer negatively impact other units or the complex as a whole?
The condo board should treat all owners consistently.
If the board allowed the installation of one washer and dryer, they would, in my opinion, be willing and able to approve the installation for others.
I am unaware of any precedent in such cases. If you really want to pursue it, you probably have to consult a lawyer: if you do, ensure you should retain a lawyer specializing in condos.