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 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; :: 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 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; :: thesis: 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; :: thesis: ( 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 ) ; :: thesis: (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; :: thesis: verum