let p, q, r be Element of CQC-WFF ; :: thesis: for X being Subset of CQC-WFF st X |- p => q holds
X |- (q => r) => (p => r)
let X be Subset of CQC-WFF ; :: thesis: ( X |- p => q implies X |- (q => r) => (p => r) )
assume A1: X |- p => q ; :: thesis: X |- (q => r) => (p => r)
X |- (p => q) => ((q => r) => (p => r)) by CQC_THE1:98;
hence X |- (q => r) => (p => r) by A1, CQC_THE1:92; :: thesis: verum