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, D being Formula of L st A \imp (B \imp C) in F & D \imp B in F holds
A \imp (D \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, D being Formula of L st A \imp (B \imp C) in F & D \imp B in F holds
A \imp (D \imp C) in F
let L be language MSAlgebra over S; :: thesis: for F being PC-theory of L
for A, B, C, D being Formula of L st A \imp (B \imp C) in F & D \imp B in F holds
A \imp (D \imp C) in F
let F be PC-theory of L; :: thesis: for A, B, C, D being Formula of L st A \imp (B \imp C) in F & D \imp B in F holds
A \imp (D \imp C) in F
let A, B, C, D be Formula of L; :: thesis: ( A \imp (B \imp C) in F & D \imp B in F implies A \imp (D \imp C) in F )
assume A1: ( A \imp (B \imp C) in F & D \imp B in F ) ; :: thesis: A \imp (D \imp C) in F
(A \imp (B \imp C)) \imp (B \imp (A \imp C)) in F by Th41;
then B \imp (A \imp C) in F by A1, Def38;
then A2: D \imp (A \imp C) in F by A1, Th45;
(D \imp (A \imp C)) \imp (A \imp (D \imp C)) in F by Th41;
hence A \imp (D \imp C) in F by A2, Def38; :: thesis: verum