let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable holds (All x,(p '&' q)) => (p '&' (All x,q)) is valid
let x be bound_QC-variable; :: thesis: (All x,(p '&' q)) => (p '&' (All x,q)) is valid
( (All x,(p '&' q)) => (p '&' q) is valid & (p '&' q) => p is valid & (p '&' q) => q is valid ) by Lm1, CQC_THE1:105;
then A1: ( (All x,(p '&' q)) => p is valid & (All x,(p '&' q)) => q is valid ) by LUKASI_1:43;
not x in still_not-bound_in (All x,(p '&' q)) by Th5;
then ( (All x,(p '&' q)) => p is valid & (All x,(p '&' q)) => (All x,q) is valid ) by A1, CQC_THE1:106;
hence (All x,(p '&' q)) => (p '&' (All x,q)) is valid by Lm3; :: thesis: verum