for Al being QC-alphabet
for A being non empty set
for x being bound_QC-variable of Al
for v being Element of Valuations_in (Al,A)
for p being Element of CQC-WFF Al
for J being interpretation of Al,A holds
( J,v |= All (x,p) iff (FOR_ALL (x,(Valid (p,J)))) . v = TRUE ) by Lm1;