let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A

for X being Subset of (CQC-WFF A) st X |- p => q holds

X |- (q => r) => (p => r)

let p, q, r be Element of CQC-WFF A; :: thesis: for X being Subset of (CQC-WFF A) st X |- p => q holds

X |- (q => r) => (p => r)

let X be Subset of (CQC-WFF A); :: 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_THE1:59;

hence X |- (q => r) => (p => r) by A1, CQC_THE1:55; :: thesis: verum

for X being Subset of (CQC-WFF A) st X |- p => q holds

X |- (q => r) => (p => r)

let p, q, r be Element of CQC-WFF A; :: thesis: for X being Subset of (CQC-WFF A) st X |- p => q holds

X |- (q => r) => (p => r)

let X be Subset of (CQC-WFF A); :: 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_THE1:59;

hence X |- (q => r) => (p => r) by A1, CQC_THE1:55; :: thesis: verum