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Let's say I have an argument with premises P, Q and R, with a conclusion S. But let's also say that Q and R are sufficient to conclude S. But having P as a premise doesn't affect the argument in any meaningful way, it's just an unnecessary premise.
If you do include P as a premise, is the argument still considered valid even if you could omit it?
Yes, if you add a redundant premise to a valid argument, the resulting argument is also valid.
If the resulting argument were invalid, that would mean that there is a case in which all the premises (say, P, Q, R) are true and the conclusion false. But then the original argument would be invalid as well, because there is a case in which its premises (Q and R) are true and the conclusion false. So adding premises cannot make a valid argument invalid.
