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, C being Formula of L holds ((A \or B) \and (A \or C)) \imp (A \or (B \and C)) 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, C being Formula of L holds ((A \or B) \and (A \or C)) \imp (A \or (B \and C)) in F
let L be language MSAlgebra over S; :: thesis: for F being PC-theory of L
for A, B, C being Formula of L holds ((A \or B) \and (A \or C)) \imp (A \or (B \and C)) in F
let F be PC-theory of L; :: thesis: for A, B, C being Formula of L holds ((A \or B) \and (A \or C)) \imp (A \or (B \and C)) in F
let A, B, C be Formula of L; :: thesis: ((A \or B) \and (A \or C)) \imp (A \or (B \and C)) in F
( B \imp (C \imp (B \and C)) in F & A \imp A in F ) by Def38, Th34;
then ( (A \or B) \imp (A \or (C \imp (B \and C))) in F & (A \or (C \imp (B \and C))) \imp ((A \or C) \imp (A \or (B \and C))) in F ) by Th59, Th79;
then A1: (A \or B) \imp ((A \or C) \imp (A \or (B \and C))) in F by Th45;
((A \or B) \imp ((A \or C) \imp (A \or (B \and C)))) \imp (((A \or B) \and (A \or C)) \imp (A \or (B \and C))) in F by Th48;
hence ((A \or B) \and (A \or C)) \imp (A \or (B \and C)) in F by A1, Def38; :: thesis: verum