let A be non empty set ; :: thesis: for v being Element of Valuations_in A
for p being Element of CQC-WFF
for J being interpretation of A holds (Valid ('not' p),J) . v = 'not' ((Valid p,J) . v)
let v be Element of Valuations_in A; :: thesis: for p being Element of CQC-WFF
for J being interpretation of A holds (Valid ('not' p),J) . v = 'not' ((Valid p,J) . v)
let p be Element of CQC-WFF ; :: thesis: for J being interpretation of A holds (Valid ('not' p),J) . v = 'not' ((Valid p,J) . v)
let J be interpretation of A; :: thesis: (Valid ('not' p),J) . v = 'not' ((Valid p,J) . v)
(Valid ('not' p),J) . v = ('not' (Valid p,J)) . v by Lm1;
hence (Valid ('not' p),J) . v = 'not' ((Valid p,J) . v) by MARGREL1:def 20; :: thesis: verum