let A be QC-alphabet ; :: thesis: for p being Element of CQC-WFF A
for x, y being bound_QC-variable of A holds (All (x,p)) => (Ex (y,p)) is valid
let p be Element of CQC-WFF A; :: thesis: for x, y being bound_QC-variable of A holds (All (x,p)) => (Ex (y,p)) is valid
let x, y be bound_QC-variable of A; :: thesis: (All (x,p)) => (Ex (y,p)) is valid
( (All (x,p)) => p is valid & p => (Ex (y,p)) is valid ) by Th15, CQC_THE1:66;
hence (All (x,p)) => (Ex (y,p)) is valid by LUKASI_1:42; :: thesis: verum