'gitlab repo without knowledge of your remote on github

I have a project which is published on Gitlab. But I also want to have it on Github as a private repo... I just have a question... if I clone it locally and then add a remote to the Github repository... this information will be accessible from the Gitlab repo? If so, how could I get it? I mean... assuming the Github remote is called remote_github and someone clones the gitlab repo locally when I run git remote it doesn't output remote_github.



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