let A be QC-alphabet ; :: thesis: for p being Element of CQC-WFF A
for x being bound_QC-variable of A holds ('not' (All (x,p))) <=> (Ex (x,('not' p))) is valid
let p be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A holds ('not' (All (x,p))) <=> (Ex (x,('not' p))) is valid
let x be bound_QC-variable of A; :: thesis: ('not' (All (x,p))) <=> (Ex (x,('not' p))) is valid
( ('not' (All (x,p))) => (Ex (x,('not' p))) is valid & (Ex (x,('not' p))) => ('not' (All (x,p))) is valid ) by Th51;
hence ('not' (All (x,p))) <=> (Ex (x,('not' p))) is valid by Lm14; :: thesis: verum