let p, q, r be Element of CQC-WFF ; :: thesis: for X being Subset of CQC-WFF st X |- p => q & X |- q => r holds
X |- p => r
let X be Subset of CQC-WFF; :: thesis: ( X |- p => q & X |- q => r implies X |- p => r )
assume that
A1: X |- p => q and
A2: X |- q => r ; :: thesis: X |- p => r
X |- (p => q) => ((q => r) => (p => r)) by CQC_THE1:59;
then X |- (q => r) => (p => r) by A1, CQC_THE1:55;
hence X |- p => r by A2, CQC_THE1:55; :: thesis: verum