At most airports you have to show your boarding pass to go through security, and then again to get on the plane. To check in you only need your passport.
I use the boarding pass on my phone screen these days, but have a print-out in my bag just in case the phone packs up on me or something else goes wrong.
At home we have an inkjet printer. I have used this in the past (back in the days before you had the barcode on your phone.) Once or twice, the airport scanner has not been able to read the inkjet printout. So, if you have access to one, print it out on a laser printer. The inkjet is possibly a little fuzzy round the edges, even though the naked eye can't tell the difference.