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 21; :: thesis: verum