let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A st not x in still_not-bound_in p holds
(p 'or' (All (x,q))) <=> (All (x,(p 'or' q))) is valid
let p, q be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A 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 of A; :: 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 Th68;
hence (p 'or' (All (x,q))) <=> (All (x,(p 'or' q))) is valid by Lm14; :: thesis: verum