JSON Schema cross key constraint support using conditonal keywords

I want to express conditional validation of schema that contains cross key conditions. Is there a support for this in JSON schema with the available conditional keywords ( allOf/anyOf/if/then/else)

JSON Schema :

{
    "type": "object",
    "additionalProperties": false,
    "properties": {
        "x": {
            "type": "object",
            "additionalProperties": false,
            "properties": {
                "value": {
                    "type": "string"
                }
            }
        },
        "y": {
            "type": "object",
            "additionalProperties": false,
            "properties": {
                "key1": {
                    "type": "string",
                    "enum": ["a", "b", "c", "d", "e"]
                },
                "key2": {
                    "type": "string",
                    "enum": ["x", "y", "m", "n", "r", "s"]
                }
            },
            "anyOf": [{
                    "allOf": [{
                            "if": {
                                "properties": {
                                    "key1": {
                                        "enum": ["a", "b"]
                                    }
                                }
                            },
                            "then": {
                                "properties": {
                                    "key2": {
                                        "enum": ["x", "y"]
                                    }
                                }
                            }
                        },
                        {
                            "if": {
                                "x": {
                                    "properties": {
                                        "value": {
                                            "const": "myVal"
                                        }
                                    }
                                }
                            },
                            "then": {
                                "properties": {
                                    "key2": {
                                        "enum": ["x", "y"]
                                    }
                                }
                            }
                        }
                    ]
                },
                {
                    "if": {
                        "properties": {
                            "key1": {
                                "enum": ["c", "d"]
                            }
                        }
                    },
                    "then": {
                        "properties": {
                            "key2": {
                                "type": "string",
                                "enum": ["m", "n"]
                            }
                        }
                    }
                }
            ]
        }
    }
}

Sample JSON instance would look like this

{
    "x": {
        "value": "myVal"
    },
    "y": {
        "key1": "a",
        "key2": "x"
    }
}

The condition that I want to express is the following 2 conditions

1. If (x.value == "myVal" AND (y.key1 == "a" OR y.key1 == "b") then y.key2 should only have "x" or "y"
   (OR)

2. If ( y.key1 == "c" OR y.key1 == "d") then y.key2 should contain only "m" or "n".

   (OR)

3. y.key2 can take any of the allowed enum values defined in y.key2 property.

The conditional I have used the JSON Schema doesn't work. I tried validating using https://www.jsonschemavalidator.net/ .

Any help would be deeply appreciated :)

Thanks