let Al be QC-alphabet ; :: thesis: for A being non empty set
for v being Element of Valuations_in (Al,A)
for p being Element of CQC-WFF Al
for J being interpretation of Al,A holds (Valid (('not' p),J)) . v = 'not' ((Valid (p,J)) . v)
let A be non empty set ; :: thesis: for v being Element of Valuations_in (Al,A)
for p being Element of CQC-WFF Al
for J being interpretation of Al,A holds (Valid (('not' p),J)) . v = 'not' ((Valid (p,J)) . v)
let v be Element of Valuations_in (Al,A); :: thesis: for p being Element of CQC-WFF Al
for J being interpretation of Al,A holds (Valid (('not' p),J)) . v = 'not' ((Valid (p,J)) . v)
let p be Element of CQC-WFF Al; :: thesis: for J being interpretation of Al,A holds (Valid (('not' p),J)) . v = 'not' ((Valid (p,J)) . v)
let J be interpretation of Al,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 19; :: thesis: verum