<xsl:apply-templates select="list[xyz[PPP]]" mode="test" />
that says apply teplates to all list elements that have an xyz child
that has a PPP child.
The list element in your input has that property so is selected and you
apply templates to it.
You don't have a template matching list so the default template applies,
which applies templates to the elements children
so templates are applied to the two xyz elements.
perhaps you want to add
<xsl:template match="list" mode="def">
something
</xsl:template>
David
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