let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable holds ((All x,p) 'or' (All x,q)) => (All x,(p 'or' q)) is valid
let x be bound_QC-variable; :: thesis: ((All x,p) 'or' (All x,q)) => (All x,(p 'or' q)) is valid
( All x,(q => (p 'or' q)) is valid & (All x,(q => (p 'or' q))) => ((All x,q) => (All x,(p 'or' q))) is valid ) by Lm6, Th26, Th34;
then A1: (All x,q) => (All x,(p 'or' q)) is valid by CQC_THE1:104;
( All x,(p => (p 'or' q)) is valid & (All x,(p => (p 'or' q))) => ((All x,p) => (All x,(p 'or' q))) is valid ) by Lm6, Th26, Th34;
then (All x,p) => (All x,(p 'or' q)) is valid by CQC_THE1:104;
hence ((All x,p) 'or' (All x,q)) => (All x,(p 'or' q)) is valid by A1, Lm7; :: thesis: verum