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 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; :: thesis: for x, y being bound_QC-variable 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; :: 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 A1: ( 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 A2: not y in still_not-bound_in (All x,p) by Th5;
(All x,p) => q is valid by A1, Th28;
hence (All x,p) => (All y,q) is valid by A2, CQC_THE1:106; :: thesis: verum