let p be Element of CQC-WFF ; :: thesis: for x, y being bound_QC-variable holds
( (Ex x,(Ex y,p)) => (Ex y,(Ex x,p)) is valid & (Ex x,y,p) => (Ex y,x,p) is valid )
let x, y be bound_QC-variable; :: thesis: ( (Ex x,(Ex y,p)) => (Ex y,(Ex x,p)) is valid & (Ex x,y,p) => (Ex y,x,p) is valid )
A1: All y,(p => (Ex x,p)) is valid by Th18, Th26;
(All y,(p => (Ex x,p))) => ((Ex y,p) => (Ex y,(Ex x,p))) is valid by Th38;
then A2: (Ex y,p) => (Ex 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 (Ex y,(Ex x,p)) by Th6;
hence (Ex x,(Ex y,p)) => (Ex y,(Ex x,p)) is valid by A2, Th22; :: thesis: (Ex x,y,p) => (Ex y,x,p) is valid
then (Ex x,y,p) => (Ex y,(Ex x,p)) is valid by QC_LANG2:20;
hence (Ex x,y,p) => (Ex y,x,p) is valid by QC_LANG2:20; :: thesis: verum