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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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