let p be Element of CQC-WFF ; for x being bound_QC-variable holds ('not' (All (x,p))) <=> (Ex (x,('not' p))) is valid
let x be bound_QC-variable; ('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 Th55;
hence
('not' (All (x,p))) <=> (Ex (x,('not' p))) is valid
by Lm14; verum