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) & X |- q holds

X |- '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) & X |- q holds

X |- 'not' p

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

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

then X |- q => ('not' p) by Th73;

hence ( not X |- q or X |- 'not' p ) by CQC_THE1:55; :: thesis: verum

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

X |- '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) & X |- q holds

X |- 'not' p

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

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

then X |- q => ('not' p) by Th73;

hence ( not X |- q or X |- 'not' p ) by CQC_THE1:55; :: thesis: verum