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
(All (x,(All (y,q)))) => (All (x,p)) 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
(All (x,(All (y,q)))) => (All (x,p)) 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
(All (x,(All (y,q)))) => (All (x,p)) 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 (All (x,(All (y,q)))) => (All (x,p)) is valid )
assume ( p = h . x & q = h . y & not y in still_not-bound_in h ) ; :: thesis: (All (x,(All (y,q)))) => (All (x,p)) is valid
then All (x,((All (y,q)) => p)) is valid by Th23, Th25;
hence (All (x,(All (y,q)))) => (All (x,p)) is valid by Th31; :: thesis: verum