let p, q be Element of CQC-WFF ; :: thesis: for h being QC-formula
for x, y being bound_QC-variable 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; :: thesis: for x, y being bound_QC-variable 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; :: 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 Th26, Th28;
hence (All x,(All y,q)) => (All x,p) is valid by Th35; :: thesis: verum