Angular 2 - Change Component variable by Service variable

I would like to change my component variable through a method performed in the service. The variable appears from true to false as desired in console.log, but is not changed in the variable set in the component. Variable to be changed: step0: boolean = true;

//SERVICE
import {
    Injectable
} from '@angular/core';

@Injectable()
export class StepsService {

    teste: string = 'texto de exemplo';
    step0: boolean;
    step1: boolean = true;

    constructor() {}

    proxStep1(): any {
        this.step0 = false;
        console.log(this.step0);
        return this.step0;
    }

    msgAlerta(): void {
        alert('Livro Angular 2 - Google - ' + this.teste);
    }
}    

//COMPONENT
import {
    Component,
    OnInit
} from '@angular/core';

import {
    StepsService
} from '../steps.service';

@Component({
    selector: 'app-step-0',
    templateUrl: './step-0.component.html',
    styleUrls: ['./step-0.component.css']
})
export class Step0Component implements OnInit {

    step0: boolean = true;

    constructor(public service: StepsService) {}

    ngOnInit() {}

    avancarStep1(): void {
        this.service.proxStep1();
    }

    enviarMsg(): void {
        this.service.msgAlerta();
    }
}

//TEMPLATE
<section class="step step0" *ngIf="step0 == true">
   <h2>Step-0 {{step0}}</h2>

   <button (click)="avancarStep1()">Avançar</button>
   <button (click)="enviarMsg()">Enviar Alerta</button>
</section>