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

for X being Subset of (CQC-WFF A) st X |- p => ('not' q) holds

X |- q => ('not' p)

let p, q be Element of CQC-WFF A; :: thesis: for X being Subset of (CQC-WFF A) st X |- p => ('not' q) holds

X |- q => ('not' p)

let X be Subset of (CQC-WFF A); :: thesis: ( X |- p => ('not' q) implies X |- q => ('not' p) )

assume A1: X |- p => ('not' q) ; :: thesis: X |- q => ('not' p)

X |- (p => ('not' q)) => (q => ('not' p)) by CQC_THE1:59;

hence X |- q => ('not' p) by A1, CQC_THE1:55; :: thesis: verum

for X being Subset of (CQC-WFF A) st X |- p => ('not' q) holds

X |- q => ('not' p)

let p, q be Element of CQC-WFF A; :: thesis: for X being Subset of (CQC-WFF A) st X |- p => ('not' q) holds

X |- q => ('not' p)

let X be Subset of (CQC-WFF A); :: thesis: ( X |- p => ('not' q) implies X |- q => ('not' p) )

assume A1: X |- p => ('not' q) ; :: thesis: X |- q => ('not' p)

X |- (p => ('not' q)) => (q => ('not' p)) by CQC_THE1:59;

hence X |- q => ('not' p) by A1, CQC_THE1:55; :: thesis: verum