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