<xsl:variable> Print out value of XSL variable using <xsl:value-of>

I'm trying to output a variable's literal string value, after it is being set depending on whether a node exists or not. I think the condition check logic is correct. But it is not outputing the values...

<xsl:variable name="subexists"/>

<xsl:template match="class">
<xsl:copy><xsl:apply-templates select="@*|node()"/></xsl:copy>
<xsl:choose>
    <xsl:when test="joined-subclass">
        <xsl:variable name="subexists" select="'true'"/>
    </xsl:when>
    <xsl:otherwise>
        <xsl:variable name="subexists" select="'false'"/>
    </xsl:otherwise>
</xsl:choose>
subexists:  <xsl:value-of select="$subexists" />

I want it to output the literal string of either "true" of "false". But it is not outputing anything. Please help! Thank you!!!

In this case no conditionals are needed to set the variable.

This one-liner XPath expression:

boolean(joined-subclass)

is true() only when the child of the current node, named joined-subclass exists and it is false() otherwise.

The complete stylesheet is:

<xsl:stylesheet version="1.0"
 xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
 <xsl:output omit-xml-declaration="yes"/>

 <xsl:template match="class">
   <xsl:variable name="subexists"
        select="boolean(joined-subclass)"
   />

   subexists:  <xsl:text/>
   <xsl:value-of select="$subexists" />
 </xsl:template>
</xsl:stylesheet>

Do note, that the use of the XPath function boolean() in this expression is to convert a node (or its absense) to one of the boolean values true() or false().