let n be non empty Nat; :: thesis: for S being non empty non void n PC-correct PCLangSignature
for L being language MSAlgebra over S
for F being PC-theory of L
for A, B being Formula of L holds (\not (A \or B)) \imp ((\not A) \and (\not B)) in F
let S be non empty non void n PC-correct PCLangSignature ; :: thesis: for L being language MSAlgebra over S
for F being PC-theory of L
for A, B being Formula of L holds (\not (A \or B)) \imp ((\not A) \and (\not B)) in F
let L be language MSAlgebra over S; :: thesis: for F being PC-theory of L
for A, B being Formula of L holds (\not (A \or B)) \imp ((\not A) \and (\not B)) in F
let F be PC-theory of L; :: thesis: for A, B being Formula of L holds (\not (A \or B)) \imp ((\not A) \and (\not B)) in F
let A, B be Formula of L; :: thesis: (\not (A \or B)) \imp ((\not A) \and (\not B)) in F
( A \imp (A \or B) in F & B \imp (A \or B) in F ) by Def38;
then A1: ( (\not (A \or B)) \imp (\not A) in F & (\not (A \or B)) \imp (\not B) in F ) by Th58;
((\not (A \or B)) \imp (\not A)) \imp (((\not (A \or B)) \imp (\not B)) \imp ((\not (A \or B)) \imp ((\not A) \and (\not B)))) in F by Th49;
then ((\not (A \or B)) \imp (\not B)) \imp ((\not (A \or B)) \imp ((\not A) \and (\not B))) in F by A1, Def38;
hence (\not (A \or B)) \imp ((\not A) \and (\not B)) in F by A1, Def38; :: thesis: verum