Filter inside of map causes undefined variable item error

[gak10100]

The following of a $filter inside of a $map results an Use of undefined variable: item error.

const result = aggregate(
  [
    {
      facilities: [
          {
              id: 123,
              name: 'abc corp'                    
          }
      ],
      existingFacilities: [
          {
              id: 456,
              companyName: 'abc corp'
          }
      ]
    }
  ],
  [
    {
      $project: {
          "facilities" : {
              "$map" : {
                  "input" : "$facilities",
                  "as" : "item",
                  "in" : {
                      "id" : "$$item.id",
                      "match" : {
                          "$arrayElemAt" : [
                              {
                                  "$filter" : {
                                      "input" : "$existingFacilities",
                                      "as" : "facility",
                                      "cond" : {
                                          "$and" : [
                                              "$$facility.companyName",
                                              {
                                                  "$eq" : ["$$facility.companyName", "$$item.name"]
                                              }
                                          ]
                                      }
                                  }
                              },
                              0
                          ]
                      },
                      "companyName" : "$$item.name"
                  }
              }
          }
      }
  }
  ]
);

console.log(result[0]);

The expected result:

{
    "facilities" : [
        {
            "id" : 123,
            "match" : {
                "id" : 456.0,
                "companyName" : "abc corp"
            },
            "companyName" : "abc corp"
        }
    ]
}