let Al be QC-alphabet ; :: thesis: for A being non empty set
for v being Element of Valuations_in (Al,A)
for p, q being Element of CQC-WFF Al
for J being interpretation of Al,A holds (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
let A be non empty set ; :: thesis: for v being Element of Valuations_in (Al,A)
for p, q being Element of CQC-WFF Al
for J being interpretation of Al,A holds (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
let v be Element of Valuations_in (Al,A); :: thesis: for p, q being Element of CQC-WFF Al
for J being interpretation of Al,A holds (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
let p, q be Element of CQC-WFF Al; :: thesis: for J being interpretation of Al,A holds (Valid ((p '&' q),J)) . v = ((Valid (p,J)) . v) '&' ((Valid (q,J)) . v)
let J be interpretation of Al,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