Natural deduction - proving that (p&q) => p is a tautology without truth tables

[r2vven]

Hello everyone!

I need to prove that [math]\vdash (p \land q) \rightarrow p[/math] is a tautology without using truth tables. However, since there's nothing to the left of the turnstile symbol, I don't know what to use as premises! Until now, I am used to having premises and using axioms and other rules of inference from there, but there are no premises here!

 

[stapel]

I need to prove that [math]\vdash (p \land q) \rightarrow p[/math] is a tautology without using truth tables. However, since there's nothing to the left of the turnstile symbol, I don't know what to use as premises! Until now, I am used to having premises and using axioms and other rules of inference from there, but there are no premises here!

Wikipedia's article on this symbol appears to provide definitions / interpretations of this symbol when nothing precedes it.

 

[blamocur]

without using truth tables.

What can you use? E.g., how is "[imath]\rightarrow[/imath]" defined you book/lectures?