Solid Hardwood, Engineered and Laminate Flooring - Removing plywood underlay

I am renovating an old bathroom and have removed a
vinyl floor covering that was glued to 1/4 inch
plywood. Although the plywood is in good condition
the surface is marred by the adhesive. I want to
install a ceramic tile but reading your expert's views
tiles do not adhere well to wood.

In addition I need to remove the 1/4 inch plywood as
adding another layer will cause problems with the height, e.g.
the shut off valve for the radiator is almost touching
the existing plywood.

Can anyone guide me regarding removing the plywood. It
has been nailed down (very securely I might add) and
although some nail heads are visible most are not.

I've thought of setting my hand saw at almost 1/4 inch
and slicing through the wood and then prying it up but
I'm wondering whether there is an easier method.

Thanks for any suggestions.

I would do exactly as you said. Use a circular saw set at just over 1/4". You should be able to cut between the joists and pry large sections up.