diff --git a/_pytest/main.py b/_pytest/main.py
index 75cb487e4..9c7266bfc 100644
--- a/_pytest/main.py
+++ b/_pytest/main.py
@@ -272,21 +272,11 @@ class Node(object):
             self._nodeid = x = self._makeid()
             return x
 
-
     def _makeid(self):
         return self.parent.nodeid + "::" + self.name
 
-    def __eq__(self, other):
-        if not isinstance(other, Node):
-            return False
-        return (self.__class__ == other.__class__ and
-                self.name == other.name and self.parent == other.parent)
-
-    def __ne__(self, other):
-        return not self == other
-
     def __hash__(self):
-        return hash((self.name, self.parent))
+        return hash(self.nodeid)
 
     def setup(self):
         pass
diff --git a/_pytest/python.py b/_pytest/python.py
index 51f887063..dd818859e 100644
--- a/_pytest/python.py
+++ b/_pytest/python.py
@@ -1087,24 +1087,6 @@ class Function(FunctionMixin, pytest.Item, FuncargnamesCompatAttr):
         super(Function, self).setup()
         fillfixtures(self)
 
-    def __eq__(self, other):
-        try:
-            return (self.name == other.name and
-                    self._args == other._args and
-                    self.parent == other.parent and
-                    self.obj == other.obj and
-                    getattr(self, '_genid', None) ==
-                    getattr(other, '_genid', None)
-            )
-        except AttributeError:
-            pass
-        return False
-
-    def __ne__(self, other):
-        return not self == other
-
-    def __hash__(self):
-        return hash((self.parent, self.name))
 
 scope2props = dict(session=())
 scope2props["module"] = ("fspath", "module")
diff --git a/testing/python/collect.py b/testing/python/collect.py
index 9d7958428..ac3892db3 100644
--- a/testing/python/collect.py
+++ b/testing/python/collect.py
@@ -287,22 +287,10 @@ class TestFunction:
             pass
         f1 = pytest.Function(name="name", parent=session, config=config,
                 args=(1,), callobj=func1)
+        assert f1 == f1
         f2 = pytest.Function(name="name",config=config,
-                args=(1,), callobj=func2, parent=session)
-        assert not f1 == f2
+                callobj=func2, parent=session)
         assert f1 != f2
-        f3 = pytest.Function(name="name", parent=session, config=config,
-                args=(1,2), callobj=func2)
-        assert not f3 == f2
-        assert f3 != f2
-
-        assert not f3 == f1
-        assert f3 != f1
-
-        f1_b = pytest.Function(name="name", parent=session, config=config,
-              args=(1,), callobj=func1)
-        assert f1 == f1_b
-        assert not f1 != f1_b
 
     def test_issue197_parametrize_emptyset(self, testdir):
         testdir.makepyfile("""