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 => (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 => r) holds

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

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

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

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

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

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

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

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

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

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

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

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