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 h & not y in still_not-bound_in p holds
(All (x,p)) => (All (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 h & not y in still_not-bound_in p holds
(All (x,p)) => (All (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 h & not y in still_not-bound_in p holds
(All (x,p)) => (All (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 h & not y in still_not-bound_in p implies (All (x,p)) => (All (y,q)) is valid )
assume ( p = h . x & q = h . y & not x in still_not-bound_in h & not y in still_not-bound_in p ) ; :: thesis: (All (x,p)) => (All (y,q)) is valid
then ( not y in still_not-bound_in (All (x,p)) & (All (x,p)) => q is valid ) by Th5, Th25;
hence (All (x,p)) => (All (y,q)) is valid by CQC_THE1:67; :: thesis: verum