Vuejs and vuex, cannot read property '$store'

I'm trying to read/access my vuex store, but I get the error "Cannot read property '$store' of undefined, why?

This is what I have tried...

I created a Vuex store in a separate store.js file.

import Vuex from "vuex";
import Vue from "vue";
import { Auth } from "aws-amplify";

Vue.use(Vuex);
export const store = new Vuex.Store({
  state: {
    user: null
  },

  actions: {
    // AWS signup action.
    async signUp({ commit }, { username, password, firstName, lastName }) {
      const data = await Auth.signUp({
        username,
        password,
        attributes: {
          given_name: firstName,
          family_name: lastName
        }
      });
      console.log(data);
    }
  }
});

Next, I registered it in my main.js Vue instance.

import Vuex from 'vuex'
import Vue from 'vue'

// Provide an initial state object for Vuex.
import store from './util/store.js';
Vue.use(Vuex)

/* eslint-disable no-new */
new Vue({
  el: '#app',
  store: store, // Vuex mechanism to "inject" the store into all child components from the root component.
  render: h => h(App),
  router
})

I try to access the store ie. console.log(this.$store) <---- cannot find this.$store

In my reg,vue:

etc
</template>
<script>
  import AppNavbar from './Layout/AppNavbar'
  import AppFooter from './Layout/AppFooter'
  import { Card, Checkbox, Button, InfoSection } from 'src/components/UIComponents';

  export default {
    components: {
      Card,
      AppNavbar,
      AppFooter,
      InfoSection,
      [Checkbox.name]: Checkbox,
      [Button.name]: Button,
    },
    data(){
      return {
        form: {
          email: '',
          password: '',
          acceptTerms: true,
          
        }
      }
    },
    methods: {
   async submitReg() {
     console.log(this.$store)
     .........