F5 Foward Proxy Vip

You can't really do ProxySSL for outbound traffic. ProxySSL requires access to the server's private key, and in most cases you won't have a remote Internet server's private key. ProxySSL also only works with non-perfect forward secret ciphers (RSA only), which is getting much harder to accommodate.

For outbound traffic, if you need to decrypt, you'd need to use SSL Forward Proxy. This is a function whereby you import a local CA certificate and private key to the F5, and that local CA re-issues (forges) remote server certificates to the local clients (that trust the local CA).

As for outbound traffic that requires a client cert, you obviously cannot decrypt this. You can't even decrypt this with ProxySSL. However in BIG-IP version 13.1, there's a client certificate detection option in SSL Forward Proxy that allows you to automcatically bypass decryption when mutual auth is detected.

And if you need to inspect the decrypted outbound traffic, I'd recommend looking at the SSL Orchestrator product, which provides all of this functionality for you.