パースの法則
hypothesis (P→Q)→Z 2. hypothesis Z→Q 3. hypothesis P 4. hypothesis Z 5. modus ponens using steps 4 and 1 Q 6. modus ponens using steps 5 and 3 P→Q 7. deduction from 4 to 6 Z 8. modus ponens using steps 7 and 2 (Z→Q)→Z 9. deduction from 3 to 8 ((Z→Q)→Z)→Z 10. Peirce's law Z 11. modus ponens using steps 9 and 10 ((P→Q)→Z)→Z 12. deduction from 2 to 11
(P→Z)→((P→Q)→Z)→Z) 13. deduction from 1 to 12 QED