TITLE: How does (wikipedia's axiomatization of) intuitionistic logic prove $p \rightarrow p$?
QUESTION [5 upvotes]: 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?

REPLY [8 votes]: $p→(p→p)$ (THEN-1)  
$p→((p→p)→p)$ (THEN-1)  
$(p→((p→p)→p))→((p→(p→p))→(p→p))$ (THEN-2)  
$(p→(p→p))→(p→p)$ (MP from lines 2,3)  
$(p→p)$ (MP from lines 1,4)