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 (A \imp 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 A \imp (B \imp (A \imp 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 A \imp (B \imp (A \imp B)) in F

let F be PC-theory of L; :: thesis: for A, B being Formula of L holds A \imp (B \imp (A \imp B)) in F

let A, B be Formula of L; :: thesis: A \imp (B \imp (A \imp B)) in F

( (B \imp (A \imp B)) \imp (A \imp (B \imp (A \imp B))) in F & B \imp (A \imp B) in F ) by Def38;

hence A \imp (B \imp (A \imp B)) in F by Def38; :: 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 (A \imp 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 A \imp (B \imp (A \imp 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 A \imp (B \imp (A \imp B)) in F

let F be PC-theory of L; :: thesis: for A, B being Formula of L holds A \imp (B \imp (A \imp B)) in F

let A, B be Formula of L; :: thesis: A \imp (B \imp (A \imp B)) in F

( (B \imp (A \imp B)) \imp (A \imp (B \imp (A \imp B))) in F & B \imp (A \imp B) in F ) by Def38;

hence A \imp (B \imp (A \imp B)) in F by Def38; :: thesis: verum