Delete element in JSONPath Java

Question

I have a JSON file like this:

{
    "objects": [{
            "type": "FirstType",
            (...)
            "details": {
                "id": 1,
                "name": "FirstElementOfTheFirstType",
                "font": "18px arial"
            },
            "id": "18e"
        },
        (...)
        {
            "type": "SecondType",
            (...)
            "details": {
                "id": 1,
                "name": "FirstElementOfTheSecondType",
                "font": "18px arial"
            },
            "id": "18f"
        }
    ],
    "background": "#ffffff"
}

My goal is to delete nodes of a certain type and id in details F.e. if I would like to delete elements of type named FirstType and id of 1.I would get:

{
    "objects": [
        (...)
        {
            "type": "SecondType",
            (...)
            "details": {
                "id": 1,
                "name": "FirstElementOfTheSecondType",
                "font": "18px arial"
            },
            "id": "18f"
        }
    ],
    "background": "#ffffff"
}

I think I partialy achieved this:

final DocumentContext jsonContext = JsonPath.parse(element.getJsonContent());
jsonContext.delete("$['objects'][?(@.type == 'FirstType')][?(@.details.id == '1')]");

But I would like to consider type and id in details as well, but I am not sure if two filter expressions are written correctly. I feel like I stuck here

EDITED: Solved

Ok. For future references, correct form goes like this:

DocumentContext jsonContext = JsonPath.parse(element.getJsonContent());
                jsonContext.delete("$['objects'][?(@.type == 'FirstType' && @.details.id == 1)]");
                element.setJsonContent(jsonContext.jsonString());