let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable st p => q is valid & not x in still_not-bound_in p holds
p => (All x,q) is valid
let x be bound_QC-variable; :: thesis: ( p => q is valid & not x in still_not-bound_in p implies p => (All x,q) is valid )
assume ( p => q is valid & not x in still_not-bound_in p ) ; :: thesis: p => (All x,q) is valid
then ( p => q in TAUT & not x in still_not-bound_in p ) by Lm13;
then p => (All x,q) in TAUT by Th34;
hence p => (All x,q) is valid by Lm13; :: thesis: verum