diff --git a/holoviews/plotting/mpl/element.py b/holoviews/plotting/mpl/element.py
index 695305bf02..4d8c86ee25 100644
--- a/holoviews/plotting/mpl/element.py
+++ b/holoviews/plotting/mpl/element.py
@@ -171,7 +171,7 @@ def _finalize_axis(self, key, element=None, title=None, dimensions=None, ranges=
                 if self.logy:
                     axis.set_yscale('log')
 
-                if not isinstance(self.projection, str) and self.projection == '3d':
+                if not (isinstance(self.projection, str) and self.projection == '3d'):
                     self._set_axis_position(axis, 'x', self.xaxis)
                     self._set_axis_position(axis, 'y', self.yaxis)
 
@@ -324,7 +324,7 @@ def _set_axis_limits(self, axis, view, subplots, ranges):
         coords = [coord if isinstance(coord, np.datetime64) or np.isreal(coord) else np.NaN for coord in extents]
         coords = [date2num(util.dt64_to_dt(c)) if isinstance(c, np.datetime64) else c
                   for c in coords]
-        if isinstance(self.projection, str) and self.projection == '3d' or len(extents) == 6:
+        if (isinstance(self.projection, str) and self.projection == '3d') or len(extents) == 6:
             l, b, zmin, r, t, zmax = coords
             if self.invert_zaxis or any(p.invert_zaxis for p in subplots):
                 zmin, zmax = zmax, zmin
diff --git a/holoviews/tests/plotting/matplotlib/test_elementplot.py b/holoviews/tests/plotting/matplotlib/test_elementplot.py
index de06cbc2a9..8e9dce71e9 100644
--- a/holoviews/tests/plotting/matplotlib/test_elementplot.py
+++ b/holoviews/tests/plotting/matplotlib/test_elementplot.py
@@ -59,6 +59,14 @@ def test_element_font_scaling_fontsize_override_specific(self):
         self.assertEqual(ax.xaxis._major_tick_kw['labelsize'], 24)
         self.assertEqual(ax.yaxis._major_tick_kw['labelsize'], 20)
 
+    def test_element_no_xaxis_yaxis(self):
+        element = Curve(range(10)).options(xaxis=None, yaxis=None)
+        axes = mpl_renderer.get_plot(element).handles['axis']
+        xaxis = axes.get_xaxis()
+        yaxis = axes.get_yaxis()
+        self.assertEqual(xaxis.get_visible(), False)
+        self.assertEqual(yaxis.get_visible(), False)
+
     def test_element_xlabel(self):
         element = Curve(range(10)).options(xlabel='custom x-label')
         axes = mpl_renderer.get_plot(element).handles['axis']