React Multistep Form State Question

FormStep1.js

var formData = {};

class FormStep1 extends Component {
	constructor(props) {
	  super(props);

	  this.state = {
	   phone: "",
	   firstname: "",
	   lastname: "",
	   disabled: false,
	   successIsVisible: false
	  }

		this.handleSubmit = this.handleSubmit.bind(this);
 	}

  handleChange(name, value){
    let state = this.state;
    state[name] = value;
    this.setState({state});
  }

  handleSubmit(e, message) {

  	this.setState({
  				phone: "",
	   			firstname: "",
	   			lastname: "",
	   			disabled: true,
	   			successIsVisible: true
  			});
  }

  render() {

  	var formBody;

  	if (this.props.visible) {
  		formBody =
  			<div>
	  			<form role="form" id="phoneForm" onSubmit={this.handleSubmit} className='row'>
					  <div className="col-md-12">
					    <div className='row'>
					      <div className="col-md-3">
					        <div className='form-group'>
					          <label htmlFor="phone">Phone</label><br />
					          <input id="phone" className="form-control" placeholder="Your Phone" onChange={this.handleChange.bind(this, 'phone')} name="phone" value={this.state.phone} />
					        </div>
					      </div>
					    </div>
					  </div>

					  <div className="col-md-12">
					    <div className='row'>
					      <div className="col-md-3">
					        <div className='form-group'>
					          <label htmlFor="firstname">Name</label><br />
					          <input id="firstname" className="form-control" placeholder="Your first name" onChange={this.handleChange.bind(this, 'firstname')} name="firstname" value={this.state.firstname} />
					        </div>
					      </div>

					      <div className="col-md-3">
					        <div className='form-group'>
					          <label htmlFor="lastname">&nbsp;</label><br />
					          <input id="lastname" className="form-control" placeholder="Your last name" onChange={this.handleChange.bind(this, 'lastname')} name="lastname" value={this.state.lastname} />
					        </div>
					      </div>
					    </div>
					  </div>

					  <div className="col-md-12">
					    <div className='row'>
					      <div className="col-md-3">
					        <button className="btn btn-green btn-block" id="btnsubmit" onSubmit={this.handleSubmit} disabled={this.state.disabled} type="submit">Vermittlung starten!</button>
					      </div>
					    </div>
					  </div>
      
					</form>
					<FormStep2 visible={this.state.successIsVisible} />
				</div>
  	}

    return (
    	<div>
	    	<CSSTransitionGroup
	        transitionName="success"
	        transitionEnterTimeout={500}
	        transitionLeaveTimeout={300}>
    			{formBody}
    		</CSSTransitionGroup>
			</div>
    );
  }
}

export default FormStep1;