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 st B in F holds

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 st B in F holds

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 st B in F holds

A \imp B in F

let F be PC-theory of L; :: thesis: for A, B being Formula of L st B in F holds

A \imp B in F

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

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

hence ( B in F implies 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 st B in F holds

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 st B in F holds

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 st B in F holds

A \imp B in F

let F be PC-theory of L; :: thesis: for A, B being Formula of L st B in F holds

A \imp B in F

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

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

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