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
A1: (All x,(p '&' q)) => (p '&' q) is valid by CQC_THE1:105;
A2: not x in still_not-bound_in (All x,(p '&' q)) by Th5;
(p '&' q) => q is valid by Lm1;
then (All x,(p '&' q)) => q is valid by A1, LUKASI_1:43;
then A3: (All x,(p '&' q)) => (All x,q) is valid by A2, CQC_THE1:106;
(p '&' q) => p is valid by Lm1;
then (All x,(p '&' q)) => p is valid by A1, LUKASI_1:43;
hence (All x,(p '&' q)) => (p '&' (All x,q)) is valid by A3, Lm3; :: thesis: verum