Does Illusion also make a Mate dissapear?

[GP11]

While playing we got into a situation where me and another guy teamed up to defeat King Tut (I think that's what he's called, I only now German names), another player plays Mate and I play Illusion on the original to substitute it with a Lvl 18 Bull Demon (again sorry if that is not it's name). My thought was that since Illusion says that the original Monster along with all cards modyfing it dissapear, the mate would also dissapear since it's created by a Card that effects the original Monster.
My friends and I are a little bit competitive so we had a heated discussion about this and would like to hear what the correct outcome would be.
Thanks!