let A be QC-alphabet ; :: thesis: for p being Element of CQC-WFF A
for x being bound_QC-variable of A holds ('not' (Ex (x,('not' p)))) <=> (All (x,p)) is valid
let p be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A holds ('not' (Ex (x,('not' p)))) <=> (All (x,p)) is valid
let x be bound_QC-variable of A; :: thesis: ('not' (Ex (x,('not' p)))) <=> (All (x,p)) is valid
( ('not' (Ex (x,('not' p)))) => (All (x,p)) is valid & (All (x,p)) => ('not' (Ex (x,('not' p)))) is valid ) by Th49;
hence ('not' (Ex (x,('not' p)))) <=> (All (x,p)) is valid by Lm14; :: thesis: verum