let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A holds
( Ex (x,(p 'or' q)) is valid iff (Ex (x,p)) 'or' (Ex (x,q)) is valid )
let p, q be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A holds
( Ex (x,(p 'or' q)) is valid iff (Ex (x,p)) 'or' (Ex (x,q)) is valid )
let x be bound_QC-variable of A; :: thesis: ( Ex (x,(p 'or' q)) is valid iff (Ex (x,p)) 'or' (Ex (x,q)) is valid )
(Ex (x,(p 'or' q))) <=> ((Ex (x,p)) 'or' (Ex (x,q))) is valid by Th41;
hence ( Ex (x,(p 'or' q)) is valid iff (Ex (x,p)) 'or' (Ex (x,q)) is valid ) by Lm15; :: thesis: verum