Is this a real e-mail from Apple?

I have had a couple phishing e-mails sent to me recently (not from Apple), but that got me concerned about other possible e-mails. I recently chatted with Apple through the online chat support and didn't login with my Apple id like I'm used to doing. Instead I just entered my name and an alternate e-mail when it asked for my information. When I was done with the chat I had the conversation sent to that e-mail and got one from AppleSupport@email.apple.com and another one from noreply@email.apple.com. Are these legitimate e-mails? Seeing email.apple.com at the end seemed a little weird.

After almost getting phished by other companies I have been worried about my computer's security.

I know I went through Apple's real website to get to the online chat, but would just like to make sure. Thank you!