How to acces Vue.prototype inside an .addEventListener?

I’m trying to access global object of Vue.prototype.$firebase which is declared in main.js

import Vue from "vue";
import App from "./App.vue";
import router from "./router";
import VueTailwind from "vue-tailwind";
import { FirebaseApp } from "@/firebase/firebase";
//Style
import "@/assets/styles/app.css";
import settings from "@/assets/styles/Tailwind.js";

FirebaseApp.auth().onAuthStateChanged((user)=>{
  Vue.prototype.$user = user;
})

//Vue
Vue.config.productionTip = false;
Vue.use(VueTailwind, settings);
Vue.prototype.$firebase = FirebaseApp;

new Vue({
  router,
  render: h => h(App)
}).$mount("#app");

inside of a Login component

<script>
export default {
  name: "Login",
  mounted: function () {
    this.submit();
  },
  methods: {
    submit() {
      let login = document.getElementById("login");     
      login.addEventListener(
        "submit",
        function (event) {
          event.preventDefault();
          const email = login.email.value;
          const password = login.password.value;
          this.$firebase
            .auth()
            .signInWithEmailAndPassword(email, password)
            .then((user) => {
              console.log(user)
              this.$router.replace('/')
            })
            .catch((error) => {
              console.log(error);
            });
        },
        true
      );
    },
  },
};
</script>

But i get TypeError: Cannot read property 'auth' of undefined, same with this.$router.
But instantiating the object outside the .addEvenListener prints well and gives me access through the let signIn, but it’s no the desire behavior i want, instead, i want to route "automatically" between a login and a dashboard on onAuthStateChange by doing the login with the Vue.prototype.$firebase instead of the local instantiation:

<script>
export default {
  name: "Login",
  mounted: function () {
    this.submit();
  },
  methods: {
    submit() {
      let login = document.getElementById("login");
      let signIn = this.$FirebaseApp;
      let onLogin = this.$router;
      login.addEventListener(
        "submit",
        function (event) {
          event.preventDefault();
          const email = login.email.value;
          const password = login.password.value;
          signIn
            .auth()
            .signInWithEmailAndPassword(email, password)
            .then((user) => {
              console.log(user)
              onLogin.replace('/')
            })
            .catch((error) => {
              console.log(error);
            });
        },
        true
      );
    },
  },
};
</script>

How is the correct way to access the Vue.prototype.$firebase and why it does have such scope limitation?