let p be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable holds
( ('not' (Ex x,p)) => (All x,('not' p)) is valid & (All x,('not' p)) => ('not' (Ex x,p)) is valid )
let x be bound_QC-variable; :: thesis: ( ('not' (Ex x,p)) => (All x,('not' p)) is valid & (All x,('not' p)) => ('not' (Ex x,p)) is valid )
A1: 'not' (Ex x,p) = 'not' ('not' (All x,('not' p))) by QC_LANG2:def 5;
hence ('not' (Ex x,p)) => (All x,('not' p)) is valid by LUKASI_1:65; :: thesis: (All x,('not' p)) => ('not' (Ex x,p)) is valid
thus (All x,('not' p)) => ('not' (Ex x,p)) is valid by A1, LUKASI_1:64; :: thesis: verum