let p, q, r be Element of HP-WFF ; :: thesis: ( p => q in HP_TAUT & q => r in HP_TAUT implies p => r in HP_TAUT )
assume that
A1: p => q in HP_TAUT and
A2: q => r in HP_TAUT ; :: thesis: p => r in HP_TAUT
(p => q) => ((q => r) => (p => r)) in HP_TAUT by Th21;
then (q => r) => (p => r) in HP_TAUT by A1, Def10;
hence p => r in HP_TAUT by A2, Def10; :: thesis: verum