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