People often claim P is true because a single book or person says P is true. This is most often the case when the book or the person is said to be divine.
So is it a fallacy when people theorise the truth of P without substantiated evidence?
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This is argument from authority.
There's an infinite number of references for this, but here's the first one from google: http://www.nizkor.org/features/fallacies/appeal-to-authority.html
The basic idea:
X is true because Y says its true.
And the argument depends on granting authority to Y. As you suggest, this can happen with religious texts, etc. But it can actually happen with anything/anyone from Stephen Hawking to Neil Degrasse Tyson to the pope to your teacher in third grade.
One thing to note for this type of fallacy is that it's what we often call an "informal fallacy" meaning it is not a fallacy of formal logic (meaning that someone has broken a rule in formal logic), but rather something we commonly believe is problematic.
To give an example, where the shoe is on the other foot:
(1) Bob says that I've got cancer. Ergo, I have cancer.
But whether this is fallacious depends on whether Bob is ...
(2) Bob is my smart friend
(2`) Bob is my local psychic
(2``) Bob is the leading oncologist in my country
Sometimes it's not an "argument from authority", but it is true because an authority says so: If you are in court and a judge says you need to pay a $100 fine, then it is true that you have to pay the fine, exactly because an authority said so :-)
Usually, if you encounter the argument, you can of course check that P is true or not independently. Alternatively, you first check whether that person or book actually said P (otherwise even the fallacy breaks down - it is a fallacy to believe something just because the bible says so, but the bible might not even say what is claimed, which would make it a false argument from authority).
Next you check whether the claimed authority is actually an authority. If it is something religious, feel free to believe it, and feel free to do what is requested from you, but don't complain if others don't believe it or laugh at you.
If the person claiming that P is true is actually an authority, and a non-biased authority, then you believe that P is true as much as you trust the authority to say what they believe is true, and to get it right. How important is it to you to know 100% whether P is true or not? Your decision if you want to spend more energy on verifying P, or trust the authority.