[{"_id":1,"array":[{"name":"name1","nestedArray":[{"value":"v1"}],"nestedArray2":[{"valueToFilter":"v1"}]},{"name":"name2","nestedArray":[{"value":"v1"},{"value":"v2"}],"nestedArray2":[{"valueToFilter":"v3"}]}]}]

db.collection.aggregate([{"$set":{"test":{"$map":{"input":"$array","as":"arr","in":{"$setIntersection":["$$arr.nestedArray.value","$$arr.nestedArray2.valueToFilter"]}}}}},{"$match":{$expr:{"$anyElementTrue":{"$map":{"input":"$test","as":"t","in":{$eq:[[],"$$t"]}}}}}},{$unset:"test"}])