Another option would be to use regular expressions and implode, like so:
if (preg_match('/'.implode('|', $array).'/', $searchstring, $matches))
echo("Yes, the string '{$matches[0]}' was found in the search string.");
else
echo("None of the strings in the array were found in the search string.");
It's a bit less code, and I would expect it to be more efficient for large search strings or arrays, since the search string will only have to be parsed once, rather than once for every element of the array. (Although you do add the overhead of the implode.)
The one downside is that it doesn't return the array index of the matching string, so the loop might be a better option if you need that. However, you could also find it with the code above followed by
$match_index = array_search($matches[0], $array);
Edit: Note that this assumes you know your strings aren't going to contain regular expression special characters. For purely alphanumeric strings like your examples that will be true, but if you're going to have more complex strings you would have to escape them first. In that case the other solution using a loop would probably be simpler.
abc4567defshould be matched or not. Do full integers need to be matched? This page is probably not suitable for closing future duplicates.