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
(Ex x,p) => (Ex x,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 y in still_not-bound_in h holds
(Ex x,p) => (Ex x,y,q) 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 (Ex x,p) => (Ex x,y,q) is valid )
assume ( p = h . x & q = h . y & not y in still_not-bound_in h ) ; :: thesis: (Ex x,p) => (Ex x,y,q) is valid
then All x,(p => (Ex y,q)) is valid by Th25, Th26;
then (Ex x,p) => (Ex x,(Ex y,q)) is valid by Th39;
hence (Ex x,p) => (Ex x,y,q) is valid by QC_LANG2:20; :: thesis: verum