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 (A \imp B) \imp ((\not B) \imp (\not A)) 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 (A \imp B) \imp ((\not B) \imp (\not A)) 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 (A \imp B) \imp ((\not B) \imp (\not A)) in F
let F be PC-theory of L; :: thesis: for A, B being Formula of L holds (A \imp B) \imp ((\not B) \imp (\not A)) in F
let A, B be Formula of L; :: thesis: (A \imp B) \imp ((\not B) \imp (\not A)) in F
(A \imp B) \imp ((A \imp (\not B)) \imp (\not A)) in F by Def38;
then A1: (A \imp (\not B)) \imp ((A \imp B) \imp (\not A)) in F by Th38;
(\not B) \imp (A \imp (\not B)) in F by Def38;
then (\not B) \imp ((A \imp B) \imp (\not A)) in F by A1, Th45;
hence (A \imp B) \imp ((\not B) \imp (\not A)) in F by Th38; :: thesis: verum