Get API ID from Serverless when using a Lambda Proxy Event

I want to pass the API ID to the "customauthorizerFunc" Lambda function as an environment var. I'm passing other information but I don't know how to reference the API ID when using a Lambda Proxy Event in a serverless.yml config. Here's an example of what I'm working with:

provider:
  name: aws
  ...
  environment:
    env: ${self:custom.stage}
    region: ${aws:region}
    awsid: ${aws:accountId}
    servicename: ${self:custom.stage}-${self:service}
    # RestApiId: !Ref ApiGatewayRestApi

functions:
  mylambdafunction:
    handler: MyLambdaFunction.lambda_handler
    ...
    events:
      - http:
          path: /thing/{thing1}
          method: get
          ...
          integration: lambda-proxy
          authorizer:
            name: customauthorizerFunc
            resultTtlInSeconds: 0
            identitySource: method.request.header.Authorization
            identityValidationExpression: NONE
            type: token

  customauthorizerFunc:
    handler: CustomAuthorizer.lambda_handler
    role: defaultrole
    timeout: 5
    memorySize: 128