let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable st not x in still_not-bound_in p holds
(p => (All x,q)) <=> (All x,(p => q)) is valid
let x be bound_QC-variable; :: thesis: ( not x in still_not-bound_in p implies (p => (All x,q)) <=> (All x,(p => q)) is valid )
assume not x in still_not-bound_in p ; :: thesis: (p => (All x,q)) <=> (All x,(p => q)) is valid
then ( (p => (All x,q)) => (All x,(p => q)) is valid & (All x,(p => q)) => (p => (All x,q)) is valid ) by Th78;
hence (p => (All x,q)) <=> (All x,(p => q)) is valid by Lm14; :: thesis: verum