let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A
for h being QC-formula of A
for x, y being bound_QC-variable of A st p = h . x & q = h . y & not y in still_not-bound_in h holds
(Ex (x,p)) => (Ex (x,y,q)) is valid
let p, q be Element of CQC-WFF A; :: thesis: for h being QC-formula of A
for x, y being bound_QC-variable of A st p = h . x & q = h . y & not y in still_not-bound_in h holds
(Ex (x,p)) => (Ex (x,y,q)) is valid
let h be QC-formula of A; :: thesis: for x, y being bound_QC-variable of A st p = h . x & q = h . y & not y in still_not-bound_in h holds
(Ex (x,p)) => (Ex (x,y,q)) is valid
let x, y be bound_QC-variable of A; :: thesis: ( p = h . x & q = h . y & not y in still_not-bound_in h implies (Ex (x,p)) => (Ex (x,y,q)) is valid )
assume ( p = h . x & q = h . y & not y in still_not-bound_in h ) ; :: thesis: (Ex (x,p)) => (Ex (x,y,q)) is valid
then All (x,(p => (Ex (y,q)))) is valid by Th22, Th23;
then (Ex (x,p)) => (Ex (x,(Ex (y,q)))) is valid by Th35;
hence (Ex (x,p)) => (Ex (x,y,q)) is valid by QC_LANG2:14; :: thesis: verum