I typically implement this with four blocks of lines in the Firewall rules:
Block1:
Allow DMZ-system to any needed destination on other VLANs
Block2:
Deny DMZ-Network to all RFC1918, this is the LAN and all other DMZs
Block3:
Allow needed traffic to "any" which is the internet in this case
Block4:
Deny DMZ-network to any
Yes, this is much easier with zones like on firepower. But it works good. And always remember that the Firewall-Rules do not control traffic to VPN-destinations. This is done in the Site-to-Site-VPN section.
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