How does (wikipedia's axiomatization of) intuitionistic logic prove $p \rightarrow p$? I'm looking at Wikipedia's article on Intuitionist logic, and I can't figure out how it would prove $(p \rightarrow p)$. Does it ...--prophetes.ai

How does (wikipedia's axiomatization of) intuitionistic logic prove $p \rightarrow p$? I'm looking at Wikipedia's article on Intuitionist logic, and I can't figure out how it would prove $(p \rightarrow p)$. Does it prove $(p \rightarrow p)$? If yes, how? If no, is there a correct (or reasonable, if there is no "correct") axiomatization of intuitionistic logic available anywhere online?

1. $p→(p→p)$ (THEN-1)
2. $p→((p→p)→p)$ (THEN-1)
3. $(p→((p→p)→p))→((p→(p→p))→(p→p))$ (THEN-2)
4. $(p→(p→p))→(p→p)$ (MP from lines 2,3)
5. $(p→p)$ (MP from lines 1,4)