Is the wall strong enough

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I'm designing a bookcase to be fit into a bungalow as the image attached.

The entire thing is made from MDF and weights collectively 180KG. There is a base cabinet sat on the floor, end panels sat on the floor, 25mm thick worktop sat on the end panels and cabinet and battens all around the walls. The wall cabinets are all half sat on the worktop and half fixed to the wall.

Loaded with books and a TV mounted in the middle will the back and side internal brick walls be strong enough to hold all this?
 

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Are you questioning the strength of the very wall you could not even drill into with an sds?:cautious:
 
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