let A be QC-alphabet ; :: thesis: 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; :: thesis: 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; :: thesis: (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; :: thesis: verum