diff --git a/src/sage/categories/sets_cat.py b/src/sage/categories/sets_cat.py
index c99f026dd0f..c1e6fb98e5a 100644
--- a/src/sage/categories/sets_cat.py
+++ b/src/sage/categories/sets_cat.py
@@ -1690,12 +1690,17 @@ def _sympy_(self):
             """
             Return an instance of a subclass of SymPy ``Set`` corresponding to ``self``.
 
+            The default implementation creates an instance of
+            :class:`~sage.interfaces.sympy_wrapper`.
+
             EXAMPLES::
 
                 sage: F = FiniteEnumeratedSets().example(); F
                 An example of a finite enumerated set: {1,2,3}
                 sage: sF = F._sympy_(); sF
                 SageSet(An example of a finite enumerated set: {1,2,3})
+                sage: sF.is_finite_set
+                True
                 sage: bool(sF)
                 True
                 sage: len(sF)
@@ -1708,6 +1713,14 @@ def _sympy_(self):
 
                 sage: RR._sympy_().is_finite_set
                 False
+
+                sage: F = Set([1, 2])
+                sage: F is Set([1, 2])
+                False
+                sage: sF = F._sympy_(); sF
+                SageSet({1, 2})
+                sage: sF._sage_() is F
+                True
             """
             from sage.interfaces.sympy_wrapper import SageSet
             return SageSet(self)
diff --git a/src/sage/interfaces/sympy_wrapper.py b/src/sage/interfaces/sympy_wrapper.py
index 35d5fed5ba1..6c22b47f9c3 100644
--- a/src/sage/interfaces/sympy_wrapper.py
+++ b/src/sage/interfaces/sympy_wrapper.py
@@ -46,6 +46,9 @@ class SageSet(Set):
     """
 
     def __new__(cls, sage_set):
+        r"""
+        Construct a wrapper for a Sage set.
+        """
         return Basic.__new__(cls, sage_set)
 
     def _sage_(self):
@@ -67,6 +70,8 @@ def _sage_(self):
     @property
     def is_empty(self):
         r"""
+        Return whether the set ``self`` is empty.
+
         EXAMPLES::
 
             sage: Empty = Set([])
@@ -79,6 +84,8 @@ def is_empty(self):
     @property
     def is_finite_set(self):
         r"""
+        Return whether the set ``self`` is finite.
+
         EXAMPLES::
 
             sage: W = WeylGroup(["A",1,1])
@@ -92,6 +99,8 @@ def is_finite_set(self):
     @property
     def is_iterable(self):
         r"""
+        Return whether the set ``self`` is iterable.
+
         EXAMPLES::
 
             sage: W = WeylGroup(["A",1,1])
@@ -105,6 +114,8 @@ def is_iterable(self):
 
     def __iter__(self):
         r"""
+        Iterator for the set ``self``.
+
         EXAMPLES::
 
             sage: sPrimes = Primes()._sympy_(); sPrimes
@@ -116,19 +127,36 @@ def __iter__(self):
         for element in self._sage_():
             yield sympify(element)
 
-    def _contains(self, other):
+    def _contains(self, element):
         """
+        Return whether ``element`` is an element of the set ``self``.
+
         EXAMPLES::
 
             sage: sPrimes = Primes()._sympy_(); sPrimes
             SageSet(Set of all prime numbers: 2, 3, 5, 7, ...)
             sage: 91 in sPrimes
             False
+
+            sage: from sympy.abc import p
+            sage: sPrimes.contains(p)
+            Contains(p, SageSet(Set of all prime numbers: 2, 3, 5, 7, ...))
+
+            sage: p in sPrimes
+            Traceback (most recent call last):
+            ...
+            TypeError: did not evaluate to a bool: None
+
         """
-        return other in self._sage_()
+        if element.is_symbol:
+            # keep symbolic
+            return None
+        return element in self._sage_()
 
     def __len__(self):
         """
+        Return the cardinality of the finite set ``self``.
+
         EXAMPLES::
 
             sage: sB3 = WeylGroup(["B", 3])._sympy_(); sB3