72 hour free transit ok with a transit within China?

Flight route:
Stockholm- Copenhagen - Beijing- Chengdu- Auckland
We are planning on getting a 72 hour free transit in Beijing but need to transit in Chengdu on our way to Auckland. We are leaving Chengdu within 72 hours from arriving in Beijing. Is this okay? I mean we are leaving from the same airport and going to a third country but there was no direct flights so this short transit in Chengdu is necessary.