The following will display it as text (with<\i class.. backslash and without ) and not as HTML, probably very simple, but I can't find it :(
<div *ngFor="let facility of facilities;">
{{facility['freewifi'] || facility['paidwifi'] ? '<\i class="fa fa-wifi fa-fw" aria-hidden="true"><\/i> :' : '' }}
</div>
Answer:
<i *ngIf="facility['freewifi'] || facility['paidwifi']" class="fa fa-wifi fa-fw" aria-hidden="true"></i>