class MyButton extends React.Component {

    constructor(props) {

        super(props);

        this.state = { count: 0 };

        this.subject = new Rx.Subject();

        this.subject

            .mapTo(1)

            .scan((origin, next) => origin + next)

            .subscribe(x => {

                this.setState({ count: x })

            })

    }

    render() {

        return <button onClick={event => this.subject.next(event)}>{this.state.count}</button>

    }

}

​

ReactDOM.render(<MyButton/>, document.getElementById('root'))