let A be QC-alphabet ; :: thesis: for p being Element of CQC-WFF A
for x being bound_QC-variable of A holds
( (All (x,('not' ('not' p)))) => (All (x,p)) is valid & (All (x,p)) => (All (x,('not' ('not' p)))) is valid )
let p be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A holds
( (All (x,('not' ('not' p)))) => (All (x,p)) is valid & (All (x,p)) => (All (x,('not' ('not' p)))) is valid )
let x be bound_QC-variable of A; :: thesis: ( (All (x,('not' ('not' p)))) => (All (x,p)) is valid & (All (x,p)) => (All (x,('not' ('not' p)))) is valid )
( All (x,(('not' ('not' p)) => p)) is valid & All (x,(p => ('not' ('not' p)))) is valid ) by Th23;
hence ( (All (x,('not' ('not' p)))) => (All (x,p)) is valid & (All (x,p)) => (All (x,('not' ('not' p)))) is valid ) by Th31; :: thesis: verum