shimano 9 & 10 speed mix

Planning to use 10 speed XT chain, cassette, rear mech and rear shifter, with 9 speed LX chainset, XT front shifter and front mech.

As I’m treating front and rear as separate systems, one all 10 speed, one all 9 speed, I’m guessing this should work fine – the 10 speed chain is only narrower on the outside so should work with the chainrings OK. Not sure if the narrower chain with wider front mech might cause problems?

This seems like the most common way of mixing of 9 and 10 speed – feedback from anyone who’s done the same gratefully received.

not sure if the chain will work on 9 speed chainset?

It will. That’ll be fine.