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