After successfully mining a block, the block and the solution is broadcast to the network. The nodes on the network in turn verify the solution. Aren't transactions that belong to the broadcasted mined block validated?
This has been covered before (I can't give links at this juncture as I'm on mobile device), but:
- each block references the previous block, preserving manipulation of blocks through POW
- each Tx references it's corresponding UTXO hash
- each UTXO requires a cryptographic puzzle (script) solution to spend the UTXOs
I'm sure someone will refer you to further information if I haven't edited this myself later on.