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 '&' ('not' p))),J)) . v = TRUE
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 '&' ('not' p))),J)) . v = TRUE
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 '&' ('not' p))),J)) . v = TRUE
let p be Element of CQC-WFF Al; :: thesis: for J being interpretation of Al,A holds (Valid (('not' (p '&' ('not' p))),J)) . v = TRUE
let J be interpretation of Al,A; :: thesis: (Valid (('not' (p '&' ('not' p))),J)) . v = TRUE
(Valid (('not' (p '&' ('not' p))),J)) . v = 'not' ((Valid ((p '&' ('not' p)),J)) . v) by Th10
.= 'not' FALSE by Th14 ;
hence (Valid (('not' (p '&' ('not' p))),J)) . v = TRUE by MARGREL1:11; :: thesis: verum