Your intuition is right; it doesn’t. It’s true whenever P is true/logically equivalent to just asserting P, which I think is the joke, but it’s not valid in general.
As an example “If ‘if it’s raining the streets are wet’ then it’s raining” is clearly false.
(Sorry if you are also participating in the joke in a way that is going over my head)
Your intuition is right; it doesn’t. It’s true whenever P is true/logically equivalent to just asserting P, which I think is the joke, but it’s not valid in general.
As an example “If ‘if it’s raining the streets are wet’ then it’s raining” is clearly false.
(Sorry if you are also participating in the joke in a way that is going over my head)
“(P → Q) → P” is intended as an argument for P.
((P → Q) → P) → P