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

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