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 \iff (\not (\not 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 \iff (\not (\not 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 \iff (\not (\not A)) in F

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

let A be Formula of L; :: thesis: A \iff (\not (\not A)) in F

A1: ((A \imp (\not (\not A))) \and ((\not (\not A)) \imp A)) \imp (A \iff (\not (\not A))) in F by Def38;

( A \imp (\not (\not A)) in F & (\not (\not A)) \imp A in F ) by Th64, Th65;

then (A \imp (\not (\not A))) \and ((\not (\not A)) \imp A) in F by Th35;

hence A \iff (\not (\not A)) in F by A1, 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 \iff (\not (\not 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 \iff (\not (\not 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 \iff (\not (\not A)) in F

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

let A be Formula of L; :: thesis: A \iff (\not (\not A)) in F

A1: ((A \imp (\not (\not A))) \and ((\not (\not A)) \imp A)) \imp (A \iff (\not (\not A))) in F by Def38;

( A \imp (\not (\not A)) in F & (\not (\not A)) \imp A in F ) by Th64, Th65;

then (A \imp (\not (\not A))) \and ((\not (\not A)) \imp A) in F by Th35;

hence A \iff (\not (\not A)) in F by A1, Def38; :: thesis: verum