Thickness of cement board on plywood ceiling
I'm building a steam shower in my basement in place of the old tub enclosure (part of redoing the bathroom).
I've ripped everything out and re-framed the walls. On the ceiling I have solid 8" joists a little irregularily spaced due to a fireplace above (It's a 1920's home). To prepare for the tiled ceiling, I screwed 3/4" plywood under the joists, and planned to put permabase cement board on that. Originally I planned for 1/2", but now I'm wondering if 1/4" is enough given that I am attaching it to 3/4" plywood. Normally ceilings are supposed to be 1/2" cement but with a plywood backing, would 1/4" not be enough? Alternately I could use 1/2" plywood and 1/2" cement board, but plywood adds more strength than cement board.
My motivation is that the ceiling is a little on the low side. Not sure if it is weakening things for 1/4" gain in height. I plan to kerdi over the whole thing, so I am wondering if that wouldn't be enough or should I stick to my original plan?