let p, q, r be Element of HP-WFF ; :: thesis: (q => r) => ((p => q) => (p => r)) in HP_TAUT
A1: (p => (q => r)) => ((p => q) => (p => r)) in HP_TAUT by Def10;
A2: ((q => r) => ((p => (q => r)) => ((p => q) => (p => r)))) => (((q => r) => (p => (q => r))) => ((q => r) => ((p => q) => (p => r)))) in HP_TAUT by Def10;
((p => (q => r)) => ((p => q) => (p => r))) => ((q => r) => ((p => (q => r)) => ((p => q) => (p => r)))) in HP_TAUT by Def10;
then (q => r) => ((p => (q => r)) => ((p => q) => (p => r))) in HP_TAUT by A1, Def10;
then A3: ((q => r) => (p => (q => r))) => ((q => r) => ((p => q) => (p => r))) in HP_TAUT by A2, Def10;
(q => r) => (p => (q => r)) in HP_TAUT by Def10;
hence (q => r) => ((p => q) => (p => r)) in HP_TAUT by A3, Def10; :: thesis: verum