• Nsross
    2
    Concerning the CP that takes place between lines 11-13. Is that a vilid use of CP? Am I allowed to assume -Q for RAA on line eleven, then Assume P for CP to prove (P -> -Q), then derive P -> -Q from 11,12 CP, despite the fact that -Q is assumed ( line 11) before we assume P for CP(line 12)?

    Hope that makes sense. Thanks!

    ¬(P→¬Q) |- (P & Q)
    1 1. ¬(P→¬Q) A
    2 2. ¬P A (aim for contradiction and use RAA to get ¬¬P)
    3 3. P A (aim for ¬Q and use CP to get (P→¬Q))
    4. 4. Q A (aim for contradiction and use RAA to get ¬Q)
    2,3 5. P&¬P 3,2 &I
    2,3 6. ¬Q 4,5 RAA
    2 7. P→¬Q 3,6 CP
    1,2 8. (P→¬Q)&¬(P→¬Q) 7,1 &I
    1 9. ¬¬P 2,8 RAA
    1 10. P 9 DN
    11 11. ¬Q A (aim for contradiction and use RAA to get ¬¬Q)
    12 12. P A (use CP to get (P→¬Q))
    11 13. (P → ¬Q) 12,11 CP
    1,11 14. (P→¬Q)&¬(P→¬Q) 13,1 &I
    1 15. ¬¬Q 11,14 RAA
    1 16. Q 15 DN
    1 17. P&Q 10,16 &I
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