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
( p => (p 'or' q) is valid & q => (p 'or' q) is valid ) by Lm6;
then A1: ( All x,(p => (p 'or' q)) is valid & All x,(q => (p 'or' q)) is valid ) by Th26;
( (All x,(p => (p 'or' q))) => ((All x,p) => (All x,(p 'or' q))) is valid & (All x,(q => (p 'or' q))) => ((All x,q) => (All x,(p 'or' q))) is valid ) by Th34;
then ( (All x,p) => (All x,(p 'or' q)) is valid & (All x,q) => (All x,(p 'or' q)) is valid ) by A1, CQC_THE1:104;
hence ((All x,p) 'or' (All x,q)) => (All x,(p 'or' q)) is valid by Lm7; :: thesis: verum