let p, q, r be Element of HP-WFF ; :: thesis: ( p => q in HP_TAUT implies (q => r) => (p => r) in HP_TAUT )
assume A1: p => q in HP_TAUT ; :: thesis: (q => r) => (p => r) in HP_TAUT
(p => q) => ((q => r) => (p => r)) in HP_TAUT by Th21;
hence (q => r) => (p => r) in HP_TAUT by A1, Def10; :: thesis: verum