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 being Formula of L holds (A \or B) \imp ((\not A) \imp B) 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 being Formula of L holds (A \or B) \imp ((\not A) \imp B) in F

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

for A, B being Formula of L holds (A \or B) \imp ((\not A) \imp B) in F

let F be PC-theory of L; :: thesis: for A, B being Formula of L holds (A \or B) \imp ((\not A) \imp B) in F

let A, B be Formula of L; :: thesis: (A \or B) \imp ((\not A) \imp B) in F

A1: A \imp ((\not A) \imp B) in F by Th56;

A2: B \imp ((\not A) \imp B) in F by Def38;

(A \imp ((\not A) \imp B)) \imp ((B \imp ((\not A) \imp B)) \imp ((A \or B) \imp ((\not A) \imp B))) in F by Def38;

then (B \imp ((\not A) \imp B)) \imp ((A \or B) \imp ((\not A) \imp B)) in F by A1, Def38;

hence (A \or B) \imp ((\not A) \imp B) in F by A2, Def38; :: thesis: verum

for L being language MSAlgebra over S

for F being PC-theory of L

for A, B being Formula of L holds (A \or B) \imp ((\not A) \imp B) 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 being Formula of L holds (A \or B) \imp ((\not A) \imp B) in F

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

for A, B being Formula of L holds (A \or B) \imp ((\not A) \imp B) in F

let F be PC-theory of L; :: thesis: for A, B being Formula of L holds (A \or B) \imp ((\not A) \imp B) in F

let A, B be Formula of L; :: thesis: (A \or B) \imp ((\not A) \imp B) in F

A1: A \imp ((\not A) \imp B) in F by Th56;

A2: B \imp ((\not A) \imp B) in F by Def38;

(A \imp ((\not A) \imp B)) \imp ((B \imp ((\not A) \imp B)) \imp ((A \or B) \imp ((\not A) \imp B))) in F by Def38;

then (B \imp ((\not A) \imp B)) \imp ((A \or B) \imp ((\not A) \imp B)) in F by A1, Def38;

hence (A \or B) \imp ((\not A) \imp B) in F by A2, Def38; :: thesis: verum