Ok I get it. Somehow I jumped to the conclusion that PPP
There is one more for your blog: A⊆ B implies B⊆ AB but not AB⊆ B (duh!)
He goes on to say he made his quantum leap to conclusions since for the quantum class BQP, PBQP=BQP, he thought the same property must hold for all classes.
I present this because he suggested it for my weblog and as a public service for those who might make a similar mistake. Yes, in case you were wondering, for reasonable classes A (like A=P), B⊆AB without needing to assume A⊆B.