1. P -> R 
2. (Q & P) v P
Conclusion R

(Q & P) v P   given premise

(QvP)&(PvP)   distributive law of v over &

(QvP)&P       idempotent law, PvP is equivalent to P

P             simplification

P -> R        given premise

P&(P -> R)    From two preceding statements

P&(~PvR)      Implication

(P&~P)v(P&R)  Distributive law of & over v

Fv(P&R)       Contradiction P&~P is equivalent to F

P&R           F is the identity for v

R             Simplification

Edwin