let n be non empty Nat; 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 in F & C \imp D in F holds
(B \imp C) \imp (A \imp D) in F
let S be 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 in F & C \imp D in F holds
(B \imp C) \imp (A \imp D) in F
let L be language MSAlgebra over S; for F being PC-theory of L
for A, B, C, D being Formula of L st A \imp B in F & C \imp D in F holds
(B \imp C) \imp (A \imp D) in F
let F be PC-theory of L; for A, B, C, D being Formula of L st A \imp B in F & C \imp D in F holds
(B \imp C) \imp (A \imp D) in F
let A, B, C, D be Formula of L; ( A \imp B in F & C \imp D in F implies (B \imp C) \imp (A \imp D) in F )
assume
( A \imp B in F & C \imp D in F )
; (B \imp C) \imp (A \imp D) in F
then
( (B \imp C) \imp (A \imp C) in F & (A \imp C) \imp (A \imp D) in F )
by Th101, Th102;
hence
(B \imp C) \imp (A \imp D) in F
by Th45; verum