let A be QC-alphabet ; 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; 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; ( 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
; (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; verum