Mutual authentication (so-called two-way SSL) for web services with PHP

Question

I'm having trouble developing how to use PHP to call SOAP when using mutual authentication.

I have my private certificate installed and running on my local server, and the end client installed the public part, and also provided me with public certificates for their system. I understand that if I used Java, I would create a client keystore (using the keytool utility) and gain access to Java (with commands such as: javax.net.ssl.trustStore, javax.net.ssl.trustStorePassword, etc. .d.), but what about PHP?

I looked at using a PHP-Java bridge, but this seems long and potentially unpleasant in itself.

I got a little confused as this mostly happens on the transport layer and there are no examples around it.