Before precising my question, here are some facts that I presume to be true:
A vaccine works by injecting the antigens of a virus into the body to train the immune system to recognize the virus and to be prepared to fight it if it shows up.
The ELISA test indirectly recognize the presence of a virus into a blood sample by testing the presence of the antigens of the virus and the antibodies that fight against it.
One of the reasons there are still no vaccine against HIV is because this virus has a very high mutation rate.
The ELISA test is used to detect the presence of HIV.
I have the feeling these facts contradict themselves and I would like to know where I am misleading.
Indeed, if we have an ELISA test for HIV, we should be able to create a vaccine because we know the antigens of the virus and we can inject a harmless version of them into our body, right? Apparently, the answer to this question is no because the HIV virus has a high mutation rate and the antibodies produced thanks to the vaccine won't be able to fight every mutation of the virus (that's the answer that gave me my former biology teacher in high school). But if the HIV has a high mutation rate, how can we be able to produce an ELISA test for it?