task: metadata: install: pip install -e .[default]
patch: diff --git a/networkx/classes/coreviews.py b/networkx/classes/coreviews.py
index a6e85213f..4769ffa71 100644
--- a/networkx/classes/coreviews.py
+++ b/networkx/classes/coreviews.py
@@ -397,7 +397,11 @@ class FilterMultiInner(FilterAdjacency):  # muliedge_seconddict
                 yield n
 
     def __getitem__(self, nbr):
-        if nbr in self._atlas and self.NODE_OK(nbr):
+        if (
+            nbr in self._atlas
+            and self.NODE_OK(nbr)
+            and any(self.EDGE_OK(nbr, key) for key in self._atlas[nbr])
+        ):
 
             def new_node_ok(key):
                 return self.EDGE_OK(nbr, key)

problem_statement: `MultiGraph` views return inconsistent `has_edge` results
### Current Behavior

Filtered views of a `MultiGraph`, created with `edge_subgraph`, return inconsistent results from `has_edge`.

### Expected Behavior

Match the same results from a `Graph`: either `True` if the edge exists in the subgraph view, or `False` if not.

### Steps to Reproduce

In case of a `MultiGraph`: checking if the edge `('a', 'c')` exists in the view may return **either `True` or `False`**.

```python
import networkx as nx

G = nx.MultiGraph()

G.add_edges_from([("a", "b"),
                  ("a", "c"),       # <-- to be filtered out
                  ("c", "b")])

H = nx.edge_subgraph(G, [("a", "b", 0), ("c", "b", 0)])

print(f"{H.edges()}\n\n"
      f"{'c' in H['a']} \t 'c' in H['a']\n"
      f"{'c' in list(H['a'])} \t 'c' in list(H['a'])\n\n"
      f"{H.has_edge('a', 'c')} \t H.has_edge('a', 'c')\n"
      f"{('a', 'c') in H.edges()} \t ('a', 'c') in H.edges()")

# [('a', 'b'), ('b', 'c')]
#
# True      H.has_edge('a', 'c')    # <-- inconsistent result
# False     ('a', 'c') in H.edges()
#
# True      'c' in H['a']           # <-- inconsistent result
# False     'c' in list(H['a'])
```

In case of a `Graph`: checking if the edge `('a', 'c')` exists in the view returns **only `False`** (as expected).

```python
import networkx as nx

G = nx.Graph()

G.add_edges_from([("a", "b"),
                  ("a", "c"),
                  ("c", "b")])

H = nx.edge_subgraph(G, [("a", "b"), ("c", "b")])

print(f"{H.edges()}\n\n"
      f"{'c' in H['a']} \t 'c' in H['a']\n"
      f"{'c' in list(H['a'])} \t 'c' in list(H['a'])\n\n"
      f"{H.has_edge('a', 'c')} \t H.has_edge('a', 'c')\n"
      f"{('a', 'c') in H.edges()} \t ('a', 'c') in H.edges()")

# [('a', 'b'), ('b', 'c')]
#
# False     H.has_edge('a', 'c')
# False     ('a', 'c') in H.edges()
#
# False     'c' in H['a']
# False     'c' in list(H['a'])
```

Note that the same results follow in case of a `DiGraph` vs. a `MultiDiGraph` object.

### Environment

Python version: `3.11.10`
NetworkX version: `3.4.2`

### Additional context

I am not sure if this is a known issue or a side-effect of edge keys in multigraphs, but thought I should report it just in case.
repo: networkx/networkx
test_cmd: pytest --no-header -rA --tb=line --color=no -p no:cacheprovider -W ignore::DeprecationWarning
test_patch: diff --git a/networkx/classes/tests/test_subgraphviews.py b/networkx/classes/tests/test_subgraphviews.py
index 73e0fdd2d..7f70b29ce 100644
--- a/networkx/classes/tests/test_subgraphviews.py
+++ b/networkx/classes/tests/test_subgraphviews.py
@@ -360,3 +360,12 @@ class TestEdgeSubGraph:
         pytest.raises(nx.NetworkXError, self.H.remove_node, 0)
         pytest.raises(nx.NetworkXError, self.H.add_edge, 5, 6)
         pytest.raises(nx.NetworkXError, self.H.remove_edge, 0, 1)
+
+    def test_consistent_edges(self):
+        # See gh-7724.
+        """Tests that the subgraph returns consistent filtered edges."""
+        G = nx.MultiDiGraph()
+        G.add_edges_from([("a", "b"), ("a", "c"), ("c", "b")])
+        H = nx.edge_subgraph(G, [("a", "b", 0), ("c", "b", 0)])
+        assert "c" not in H["a"]
+        assert not H.has_edge("a", "c")