Depends on what you mean by "perfectly fine" ... if the student understands that they deduced the desired conclusion from the true fact 0=0, by a series of step

Depends on what you mean by "perfectly fine" ... if the student understands that they deduced the desired conclusion from the true fact 0=0, by a series of steps of the form "our current statement is implied by this next statement, which is implied by the next, which is implied by ... 0=0, which is known to be true", then I guess it's ok other than being an obfuscated/roundabout proof technique.