Don't think you can get to "just the WHERE clause" per se, but you can get the source code of all the desired SProcs using something like:
FROM sys.objects AS O
JOIN sys.sql_modules AS M
ON M.object_id = O.object_id
WHERE O.type = 'P'
AND O.name IN ('MySProc1', 'MySProc2')
One snag you might have is if the [definition] is truncated. Depending on what SQL tool you are using (and how it is configured) then all columns may be truncated at 255, or 8,000 characters. If that's a problem for you then you would have to find a way to work around that [e.g. check the CONFIG Max Column Length] (or look at each one in turn of course).
If you are looking for "something in particular" in the WHERE clause then you could add
AND M.definition LIKE '%SomeUniqueSnippet%'