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1.:: [(P --> Q) & P ] Conditional proof (CP) assumption #1
2.:: P 1 Simplification (SIMP)
3.:: (P --> Q) 1 SIMP
4.:: Q 2,3 Modus Ponens (MP)
5.:: [(P --> Q) & P ] --> Q 1-4, CP
6. [(P --> Q) & P ] --> Q 1-5, CP (discharges CP assumptions)