let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A st Ex (x,(p '&' q)) is valid holds
(Ex (x,p)) '&' (Ex (x,q)) is valid
let p, q be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A st Ex (x,(p '&' q)) is valid holds
(Ex (x,p)) '&' (Ex (x,q)) is valid
let x be bound_QC-variable of A; :: thesis: ( Ex (x,(p '&' q)) is valid implies (Ex (x,p)) '&' (Ex (x,q)) is valid )
assume A1: Ex (x,(p '&' q)) is valid ; :: thesis: (Ex (x,p)) '&' (Ex (x,q)) is valid
(Ex (x,(p '&' q))) => ((Ex (x,p)) '&' (Ex (x,q))) is valid by Th43;
hence (Ex (x,p)) '&' (Ex (x,q)) is valid by A1, CQC_THE1:65; :: thesis: verum