nginx proxy_pass and docker – I don’t want port number in address bar

On mywebsite.com, I have running docker container with wordpress.
I started it as

docker run -p 8000:80 --name docker-wordpress-nginx -d 

and

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docker ps

shows

0.0.0.0:8000->80/tcp

and on my host I have nginx running with

server {
     listen   80;
...
server_name mywebsite.com www.mywebsite.com;
...
location / {
             proxy_pass http://localhost:8000/;
             proxy_set_header Host $host;
    }

when i go here

mywebsite.com

It brings wordpress index page of my site, but address in browser is now

mywebsite.com:8000

instead of

mywebsite.com

which I expected.
Everything looks as i wanted except that I always get that port number in address

http://mywebsite.com:8000/2015/08/01/hello-world/

Instead, I wanted

http://mywebsite.com/2015/08/01/hello-world/

i mean, in general, instead of

http://mywebsite.com:8000/some_blog/

i want

http://mywebsite.com/some_blog/

Any ideas?

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