let A be non empty set ; :: thesis: for v being Element of Valuations_in A
for p, q being Element of CQC-WFF
for J being interpretation of A holds (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
let v be Element of Valuations_in A; :: thesis: for p, q being Element of CQC-WFF
for J being interpretation of A holds (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
let p, q be Element of CQC-WFF ; :: thesis: for J being interpretation of A holds (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
let J be interpretation of A; :: thesis: (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
(Valid ((p '&' q),J)) . v = ((Valid (p,J)) '&' (Valid (q,J))) . v by Lm1;
hence (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v) by MARGREL1:def 20; :: thesis: verum