THEOREM
*******
~A => [A => B] (Truth Table,
lines 3-4)
PROOF
*****
Suppose...
1 ~A
Premise
Suppose...
2 A
Premise
Suppose to the
contrary...
3 ~B
Premise
Obtain
contradiction...
4 A & ~A
Join, 2, 1
Apply Conclusion
Rule (By Contradiction)
5 ~~B
4 Conclusion, 3
Apply Double Negation Rule
6 B
Rem DNeg,
5
Apply Conclusion Rule
(Direct Proof)
7 A => B
4 Conclusion, 2
Apply Conclusion Rule (Direct Proof)
As Required:
8 ~A => [A => B]
4 Conclusion, 1