Redirect changing page URL but not rendering new page

I have a page that validates a user and redirects them to a login page if validation is successful. However, the using redirect the URL changes but the new page for Login is not rendered. How can I get the new page to render?

App.js

var child;

render() {
if (this.state.toLogin && !this.state.mounted) {
    <Route exact path="/Login" component={Login} />;
    <Route exact strict path="/" render={({location}) => {
       if (location.pathname === window.location.pathname) {
             return <Redirect to="/Login"/>;
        }
    return null;
}}

return(
    <div className="App">
        <ReactCSSTransitionGroup
            transitionName="remove"
            transitionEnterTimeout={100}
            transitionLeaveTimeout={100}>
                {child}
        </ReactCSSTransitionGroup>
    </div>
    );
}

Index.js

ReactDOM.render(
  <BrowserRouter>
    <App />
  </BrowserRouter>,
  document.getElementById('root')
);

EDIT: Made changes as per answers but now the URL is not changing and the page is not rendering

from Redirect changing page URL but not rendering new page