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 st A \imp B in F holds
(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 st A \imp B in F holds
(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 st A \imp B in F holds
(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 st A \imp B in F holds
(B \imp C) \imp (A \imp C) in F
let A, B, C be Formula of L; :: thesis: ( A \imp B in F implies (B \imp C) \imp (A \imp C) in F )
(A \imp B) \imp ((B \imp C) \imp (A \imp C)) in F by Th39;
hence ( A \imp B in F implies (B \imp C) \imp (A \imp C) in F ) by Def38; :: thesis: verum