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