let A be non empty set ; :: thesis: for p being Element of CQC-WFF
for J being interpretation of A holds Valid ((p '&' p),J) = Valid (p,J)
let p be Element of CQC-WFF ; :: thesis: for J being interpretation of A holds Valid ((p '&' p),J) = Valid (p,J)
let J be interpretation of A; :: thesis: Valid ((p '&' p),J) = Valid (p,J)

now

let v be Element of Valuations_in A; :: thesis: (Valid ((p '&' p),J)) . v = (Valid (p,J)) . v
thus (Valid ((p '&' p),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (p,J)) . v) by Th22
.= (Valid (p,J)) . v ; :: thesis: verum

end;

hence Valid ((p '&' p),J) = Valid (p,J) by FUNCT_2:113; :: thesis: verum