theorem :: AOFA_L00:138

for n being non empty Nat
for J being non empty non void Signature
for T being non-empty MSAlgebra over J
for X being empty-yielding GeneratorSet of T
for S1 being non empty non void b₂ -extension b₁ PC-correct QC-correct QCLangSignature over Union X
for L being non-empty Language of X extended_by ({}, the carrier of S1),S1
for G being QC-theory of L
for A, B being Formula of L
for x being Element of Union X
for a being SortSymbol of J st L is subst-correct & L is vf-qc-correct & x in X . a & x nin (vf A) . a holds
(\ex (x,(A \imp B))) \imp (A \imp (\ex (x,B))) in G