let p, q, r, s be Element of HP-WFF ; :: thesis: (p => (q => r)) => ((s => q) => (p => (s => r))) in HP_TAUT
A1: (((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s => r))) in HP_TAUT by Lm4;
((((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s => r)))) => ((p => (q => r)) => ((s => q) => (p => (s => r)))) in HP_TAUT by Lm4;
hence (p => (q => r)) => ((s => q) => (p => (s => r))) in HP_TAUT by A1, Def10; :: thesis: verum