PVP unlocked skills and relation with PVE unlocked skills question

the story:
i unlocked some skills for monk on my PVP ele, then i made a PVE monk in factions, i went to the skill trainer and i found the skills i unlocked for monk in pvp already unlocked at the skill trainer.......i did this for some other classes too.

now the question, if i already made a pve monk, then i unlocked some monk skills in pvp, and i switch to the pve monk and go to the skill trainer, will the new unlocked skills in pvp be available for the pve monk??

Short answer: yes.

Yes, this works the best for Prophecies and Nightfall skills that come available late in the game. You can unlock them with pvp faction, and they become available to all skill trainers from the correct campaign.

Any non elite skill you unlock on your account(by any means), becomes available to purchase at any skill trainer from the campaign the skill belongs to.

When you unlock a skill, it becomes unlocked for everyone on your account, and all your heroes can use the skill without further purchase.

Your characters, however, will still need to purchase the skill from a skill trainer on the continent where the skill is available.

In addition, if you have beaten a particular campaign, unlocked skills from that campaign will be available to all your characters on that account at all skill trainers in that campaign. If you HAVEN'T beaten that campaign, then some skills will only be available for purchase at particular skill trainers. (Previous two replies didn't mention that condition).