The Duke of Sussex's cross-examination continued Wednesday ... where his lengthy witness statement was picked apart -- namely, pointing to the fact the guy hasn't brought any actual evidence of phone hacking, including alleged data Harry has cited.

Harry's explanation for this, so far, has been his suspicion that the Daily Mirror journos he alleges were spying on him/hacking his phone were probably using burners to cover their tracks ... plus the fact all this stuff happened so long ago, well over a decade at this point.

Then, some nitty gritty ... the opposing attorney, Andrew Green, went through several different stories that are at the center of the case -- and he broke down, one by one, why Harry thought phone hacking and/or spying was at the center of these gossipy pieces.

For example, a few articles were brought up from the mid-2000s referencing his relationship with his ex-GF Chelsy Davy -- details of which the Mirror reported on back then, including break-ups/ ups and down they'd gone through, which PH believes were reported on via illegal news-gathering tactics.

However, when pressed on why he thought that, he revealed that the unnamed "palace" sources cited in the stories couldn't have known about those things ... because he says he never discussed those things with any palace officials. There are also details from phone calls the two had that were reported on -- which cited friends as the source -- and Harry said he thought those were hacked from his voice mails.

What Green pointed out, however, is that a lot of these stories the Mirror did were actually out in other outlets too -- and sometimes even originated from other outlets, including American gossip mags -- and that they often cited anonymous sources who claimed to be in the know. What Green was getting at ... perhaps people in Harry's inner circle and/or people who worked for or with the palace provided the info, without any hacking whatsoever.

Essentially, Green was making the point that it's quite commonplace for outlets to get what some might consider inside info from well-placed sources ... and that citing anonymous sources is, oftentimes, exactly how a tabloid publication may have gotten the scoop.

Harry pushed back though ... insisting much of the content reported on by DM could've only been obtained by accessing his private records/correspondence. Green said Harry was "living in a land of total speculation" about where the info might've actually come from -- and Harry said he disagreed. They also butted heads at other points in the cross ... at one point, Green interrupted Harry (who kept turning to the judge) to say -- "Could I ask the questions?"

Long story short ... Green was making the case that a lot of what Harry's griping about had either already been out and reported on, usually citing anonymous sources, or that the Daily Mirror's stories were reported on with info that was easily accessible to the public. Harry called BS on that -- but when pressed on deets, he didn't seem to have any smoking gun. Just a lot of conviction and firm belief -- which Green consistently questioned and doubted.