let p, q be Element of HP-WFF ; :: thesis: ((p => q) '&' p) => q in HP_TAUT
set P = p => q;
A1: (p => q) => (p => q) in HP_TAUT by Th14;
((p => q) => (p => q)) => (((p => q) '&' p) => q) in HP_TAUT by Th34;
hence ((p => q) '&' p) => q in HP_TAUT by A1, Def10; :: thesis: verum