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 'or' (All x,q)) <=> (All x,(p 'or' q)) is valid
let x be bound_QC-variable; :: thesis: ( not x in still_not-bound_in p implies (p 'or' (All x,q)) <=> (All x,(p 'or' q)) is valid )
assume not x in still_not-bound_in p ; :: thesis: (p 'or' (All x,q)) <=> (All x,(p 'or' q)) is valid
then ( (p 'or' (All x,q)) => (All x,(p 'or' q)) is valid & (All x,(p 'or' q)) => (p 'or' (All x,q)) is valid ) by Th72;
hence (p 'or' (All x,q)) <=> (All x,(p 'or' q)) is valid by Lm14; :: thesis: verum