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 that
A1: p => q is valid and
A2: not x in still_not-bound_in p ; :: thesis: p => (All x,q) is valid
A3: p => q in TAUT by A1, Lm13;
A4: p => (All x,q) in TAUT by A2, A3, Th34;
thus p => (All x,q) is valid by A4, Lm13; :: thesis: verum