4.4 Demonstration of the Equivalence

Concerning the demonstrating method for p iff q (p <=> q), p implies q is demonstrated first, then q implies p is demonstrated. The system automatically interprets p iff q as p implies q & q implies p. Therefore, if we state that p implies q, the first half is considered to be demonstrated. The rest is the other half's demonstration. As a result, with assume q, it becomes thus p and it is judged that p iff q is said.

     p iff q
          assume p;
          thus q;
 p => q could be said
          assume q;
          thus p;
 q => p can be said and p <=> q