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, C being Formula of L holds (A \imp B) \imp ((B \imp C) \imp (A \imp C)) 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, C being Formula of L holds (A \imp B) \imp ((B \imp C) \imp (A \imp C)) in F
let L be language MSAlgebra over S; :: thesis: for F being PC-theory of L
for A, B, C being Formula of L holds (A \imp B) \imp ((B \imp C) \imp (A \imp C)) in F
let F be PC-theory of L; :: thesis: for A, B, C being Formula of L holds (A \imp B) \imp ((B \imp C) \imp (A \imp C)) in F
let A, B, C be Formula of L; :: thesis: (A \imp B) \imp ((B \imp C) \imp (A \imp C)) in F
(B \imp C) \imp ((A \imp B) \imp (A \imp C)) in F by Th37;
hence (A \imp B) \imp ((B \imp C) \imp (A \imp C)) in F by Th38; :: thesis: verum