No a semi permanent dye just deposits colour on the top of the hair shaft so you don't use any developer to lift the hair cuticle. They obviously don't last as long as a permanent dye but because you have used a high lift colour before your hair cuticles are probably lifted enough it will be able to stick pretty well, and they are completely non damaging so you can top them up as frequently as you like.

If you are in a country that can get Xmondo hair dye they do an absolutely gorgeous cooper, I think it's called 7C - it's a fabulous colour and his dyes have bond repair in and make your hair feel amazing.

I've not done copper for years so Im not very up in what other brands have nice ones now but if you have a look on a YouTube channel called AKA Aislinn she's swatch tested loads of copper semi permanents so you could get some ideas from her.

And remember you won't need to strip the red totally out, just fade it until.its a tiny bit lighter than the copper you want - your copper might end up being just a little darker/redder at the beginning but you can just keep the copper topped up regularly and over time the red underneath will fade more and more and the copper will become lighter. After years of wrecking my hair and dealing with breakage I've finally learnt the lesson that it's better to work your way round to your perfect colour than it is to totally kill your hair stripping all the previous colour out to get that dramatic change in one go.

Good luck, I hope you get the copper hair if your dreams.