Is P45 necessary for Jobseekers Allowance? Misplaced it

I submitted an application for JSA about 3 weeks ago after finishing college and I received a letter asking me to come in for an interview about the application. Among the list of items to bring is the "P45 from my last place of employment".

My last 'employment' was for 3 months in the summer of 2016 in which I worked in my university under a research grant, but I'm not sure if this counts as employment for the process and there was no P45/any documents.

Before that I worked 2013-2014 in a supermarket and did receive a P45 but cannot find it anywhere! I have payslips, P60s for the 2 years and can get P21s on the Revenue website. Are these any good to me or is it the P45 or nothing?