As others have said you should probably use a class rather than an id, unless you have a very good reason for it.
Here is the code for changing the id
$( "li > a" ).click(function() {
$('#current').removeAttr( 'id','current');
$( this ).attr('id', 'current');
});
or the class instead..
$( "li > a" ).click(function() {
$('.current').removeAttr( 'class','current');
$( this ).attr('class', 'current');
});
And here is your modified jsfiddle http://jsfiddle.net/39rc2Le5/2/
Update
If you use the class instead you will have something like this...
<nav>
<ul>
<li><a class="current" href="#">A</a>
</li>
<li><a class="" href="#3">B</a>
</li>
<li><a class="" href="#"> C</a>
</li>
<li><a class="" href="#"> D</a>
</li>
<li><a class="" href="#"> E</a>
</li>
<li><a class="" href="#"> F</a>
</li>
</ul>
</nav>
Then your tabs which are currently styled by a#current
properties would be styled by a.current
properties. So change your css selector like this.
nav ul li a.current {
background-color: #F9F9F9;
border-style: solid;
border-color: #ee1d78;
border-top: 15px;
border-left: none;
border-right: none;
}