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) => r holds

X |- q => r

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

X |- q => r

let X be Subset of (CQC-WFF A); :: thesis: ( X |- (p => q) => r implies X |- q => r )

assume A1: X |- (p => q) => r ; :: thesis: X |- q => r

X |- ((p => q) => r) => (q => r) by CQC_THE1:59;

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

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

X |- q => r

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

X |- q => r

let X be Subset of (CQC-WFF A); :: thesis: ( X |- (p => q) => r implies X |- q => r )

assume A1: X |- (p => q) => r ; :: thesis: X |- q => r

X |- ((p => q) => r) => (q => r) by CQC_THE1:59;

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