let Al be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF Al
for x being bound_QC-variable of Al st p => q is valid & not x in still_not-bound_in p holds
p => (All (x,q)) is valid
let p, q be Element of CQC-WFF Al; :: thesis: for x being bound_QC-variable of Al 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 of Al; :: 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
p => q in TAUT Al by A1, Lm13;
then p => (All (x,q)) in TAUT Al by A2, Th13;
hence p => (All (x,q)) is valid by Lm13; :: thesis: verum