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

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

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

A1: ((B \imp A) \imp (B \imp A)) \imp (B \imp ((B \imp A) \imp A)) in F by Th41;

(B \imp A) \imp (B \imp A) in F by Th34;

hence B \imp ((B \imp A) \imp A) in F by A1, 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 B \imp ((B \imp A) \imp 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 B \imp ((B \imp A) \imp 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 B \imp ((B \imp A) \imp A) in F

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

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

A1: ((B \imp A) \imp (B \imp A)) \imp (B \imp ((B \imp A) \imp A)) in F by Th41;

(B \imp A) \imp (B \imp A) in F by Th34;

hence B \imp ((B \imp A) \imp A) in F by A1, Def38; :: thesis: verum