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 ((\not A) \or (\not B)) \imp (\not (A \and 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 ((\not A) \or (\not B)) \imp (\not (A \and 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 ((\not A) \or (\not B)) \imp (\not (A \and B)) in F

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

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

( (A \and B) \imp A in F & (A \and B) \imp B in F ) by Def38;

then A1: ( (\not A) \imp (\not (A \and B)) in F & (\not B) \imp (\not (A \and B)) in F ) by Th58;

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

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

hence ((\not A) \or (\not B)) \imp (\not (A \and B)) in F by A1, 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 ((\not A) \or (\not B)) \imp (\not (A \and 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 ((\not A) \or (\not B)) \imp (\not (A \and 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 ((\not A) \or (\not B)) \imp (\not (A \and B)) in F

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

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

( (A \and B) \imp A in F & (A \and B) \imp B in F ) by Def38;

then A1: ( (\not A) \imp (\not (A \and B)) in F & (\not B) \imp (\not (A \and B)) in F ) by Th58;

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

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

hence ((\not A) \or (\not B)) \imp (\not (A \and B)) in F by A1, Def38; :: thesis: verum