Indeed.
The war was entirely a panicked misadventure by the British and French over their empires in the far east.
Hitler is on their side, against Mussolini, then Hitler flips to Mussolini's side.
Soon as Hitler flips they take the next opportunity to declare war.
The whole war was about Suez, to include the war against the Japanese.
Suez is the global linchpin holding the empires together.