let A be QC-alphabet ; 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 x in still_not-bound_in q & not y in still_not-bound_in h holds
(Ex (x,p)) => (Ex (y,q)) is valid
let p, q be 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 x in still_not-bound_in q & not y in still_not-bound_in h holds
(Ex (x,p)) => (Ex (y,q)) is valid
let h be QC-formula of A; for x, y being bound_QC-variable of A st p = h . x & q = h . y & not x in still_not-bound_in q & not y in still_not-bound_in h holds
(Ex (x,p)) => (Ex (y,q)) is valid
let x, y be bound_QC-variable of A; ( p = h . x & q = h . y & not x in still_not-bound_in q & not y in still_not-bound_in h implies (Ex (x,p)) => (Ex (y,q)) is valid )
assume
( p = h . x & q = h . y & not x in still_not-bound_in q & not y in still_not-bound_in h )
; (Ex (x,p)) => (Ex (y,q)) is valid
then
( not x in still_not-bound_in (Ex (y,q)) & p => (Ex (y,q)) is valid )
by Th6, Th22;
hence
(Ex (x,p)) => (Ex (y,q)) is valid
by Th19; verum