let p be Element of CQC-WFF ; :: thesis: for x, y being bound_QC-variable holds (Ex x,(All y,p)) => (All y,(Ex x,p)) is valid
let x, y be bound_QC-variable; :: thesis: (Ex x,(All y,p)) => (All y,(Ex x,p)) is valid
A1: All y,(p => (Ex x,p)) is valid by Th18, Th26;
(All y,(p => (Ex x,p))) => ((All y,p) => (All y,(Ex x,p))) is valid by Th34;
then A2: (All y,p) => (All y,(Ex x,p)) is valid by A1, CQC_THE1:104;
not x in still_not-bound_in (Ex x,p) by Th6;
then not x in still_not-bound_in (All y,(Ex x,p)) by Th5;
hence (Ex x,(All y,p)) => (All y,(Ex x,p)) is valid by A2, Th22; :: thesis: verum