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 (\not B)) \imp (\not (A \and 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 (\not B)) \imp (\not (A \and 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 (\not B)) \imp (\not (A \and B)) in F
let F be PC-theory of L; :: thesis: for A, B being Formula of L holds ((\not A) \or (\not B)) \imp (\not (A \and B)) in F
let A, B be Formula of L; :: thesis: ((\not A) \or (\not B)) \imp (\not (A \and B)) in F
( (A \and B) \imp A in F & (A \and B) \imp B in F ) by Def38;
then A1: ( (\not A) \imp (\not (A \and B)) in F & (\not B) \imp (\not (A \and B)) in F ) by Th58;
((\not A) \imp (\not (A \and B))) \imp (((\not B) \imp (\not (A \and B))) \imp (((\not A) \or (\not B)) \imp (\not (A \and B)))) in F by Def38;
then ((\not B) \imp (\not (A \and B))) \imp (((\not A) \or (\not B)) \imp (\not (A \and B))) in F by A1, Def38;
hence ((\not A) \or (\not B)) \imp (\not (A \and B)) in F by A1, Def38; :: thesis: verum