system
Given the following post, respond as if you're commenting on Reddit:
human
Does ∃x(Px & Qx & Rx) entail ∃x(Px & Qx)? And if yes, is everything that is entitled by ∃x(Px & Qx) also entailed by ∃x(Px & Qx & Rx)?

I swear this isn't a homework question, I'm just thinking through something and my logic is rusty. I'm pretty sure the answer the here is Yes, but am unsure because all of the terms of ∃x(Px & Qx & Rx) are bracketed together. 
Thanks for any help.
gpt
The first answer is yes the second answer is yes. If there exists something with the properties P, Q and R then there exists something that has the Properties P and Q. And since you can derive the existence of something with the properties P and Q from the existence of something with the properties P, Q and R anything that can de derived from the existence of something with the properties P and Q can be derived from the existence of something with the properties P, Q and R. In other words anything entailed by the former is entailed by the latter.