"Caller does not have permissions to execute the stored procedure" based on sys procedure

Did create the following procedure on my DB to read SQL Server Log:

USE [MyDB]
GO

ALTER PROCEDURE [OMEGACA].[P_SYS_READ_POL_DEBUG] ( 
    @p_log_no int,
    @p_search_1 nvarchar(4000),
    @p_search_2 nvarchar(4000)
    )
AS

BEGIN

EXEC sys.sp_readerrorlog @p_log_no, 1, @p_search_1, @p_search_2 ;

END;

Schema, DB user and Login is granted server role "sysadmin".

Execute on the above procedure is granted to a certain MyDB's role. 
This role is granted to a certain DB user X (and login).

When this user tries to execute the procedure above, it receives error:
Caller does not have permissions to execute the stored procedure based on sys procedure

Question:
How can I get the needed permission for user X?

ps. Granting sysadmin to X is not liked.