let p be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable holds (All (x,('not' p))) <=> ('not' (Ex (x,p))) is valid
let x be bound_QC-variable; :: thesis: (All (x,('not' p))) <=> ('not' (Ex (x,p))) is valid
('not' ('not' (All (x,('not' p))))) => (All (x,('not' p))) is valid ;
then A1: ('not' (Ex (x,p))) => (All (x,('not' p))) is valid by QC_LANG2:def 5;
(All (x,('not' p))) => ('not' ('not' (All (x,('not' p))))) is valid ;
then (All (x,('not' p))) => ('not' (Ex (x,p))) is valid by QC_LANG2:def 5;
hence (All (x,('not' p))) <=> ('not' (Ex (x,p))) is valid by A1, Lm14; :: thesis: verum