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 being Formula of L holds A \imp (A \and 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 being Formula of L holds A \imp (A \and A) in F

let L be language MSAlgebra over S; :: thesis: for F being PC-theory of L

for A being Formula of L holds A \imp (A \and A) in F

let F be PC-theory of L; :: thesis: for A being Formula of L holds A \imp (A \and A) in F

let A be Formula of L; :: thesis: A \imp (A \and A) in F

A1: (A \imp A) \imp ((A \imp A) \imp (A \imp (A \and A))) in F by Th49;

A2: A \imp A in F by Th34;

then (A \imp A) \imp (A \imp (A \and A)) in F by A1, Def38;

hence A \imp (A \and A) in F by A2, Def38; :: thesis: verum

for L being language MSAlgebra over S

for F being PC-theory of L

for A being Formula of L holds A \imp (A \and 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 being Formula of L holds A \imp (A \and A) in F

let L be language MSAlgebra over S; :: thesis: for F being PC-theory of L

for A being Formula of L holds A \imp (A \and A) in F

let F be PC-theory of L; :: thesis: for A being Formula of L holds A \imp (A \and A) in F

let A be Formula of L; :: thesis: A \imp (A \and A) in F

A1: (A \imp A) \imp ((A \imp A) \imp (A \imp (A \and A))) in F by Th49;

A2: A \imp A in F by Th34;

then (A \imp A) \imp (A \imp (A \and A)) in F by A1, Def38;

hence A \imp (A \and A) in F by A2, Def38; :: thesis: verum