Diferent behaviour using document() in IE / FF

I have this strange behaviour using XSLT in IE and FF.

I have a XML like this:
<doc>
<aaa>
<bbb>ccc</bbb>
</aaa>
<ccc>
<ddd>eee</eee>
</ccc>
</doc>

In the client (browser) i load this documento and apply a xslt so it
results in this:

<doc>
<aaa>
<bbb>ccc</bbb>
</aaa>
</doc>

Sometime later in the application, i use another xslt that uses that
document (call it "doc.xml")

<xsl:variable name="xmldoc" select="document('doc.xml')"/>
<xsl:apply-templates select="$xmldoc"/>

what happens is that teh content of the variable xmldoc is, in IE, the
original document, as i expected

<doc>
<aaa>
<bbb>ccc</bbb>
</aaa>
<ccc>
<ddd>eee</eee>
</ccc>
</doc>

but in FF i get the first transformed doc

<doc>
<aaa>
<bbb>ccc</bbb>
</aaa>
</doc>

Since i want to access the nodes on the original doc (in this example
<ccc>), in FF my app won't work.

I'm wondering  what the correct behaviour should be, or is this
implementation dependent?

Thanks.