let A be QC-alphabet ; for p being Element of CQC-WFF A
for x being bound_QC-variable of A holds (Ex (x,('not' ('not' p)))) <=> (Ex (x,p)) is valid
let p be Element of CQC-WFF A; for x being bound_QC-variable of A holds (Ex (x,('not' ('not' p)))) <=> (Ex (x,p)) is valid
let x be bound_QC-variable of A; (Ex (x,('not' ('not' p)))) <=> (Ex (x,p)) is valid
( (Ex (x,('not' ('not' p)))) => (Ex (x,p)) is valid & (Ex (x,p)) => (Ex (x,('not' ('not' p)))) is valid )
by Th47;
hence
(Ex (x,('not' ('not' p)))) <=> (Ex (x,p)) is valid
by Lm14; verum