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