theorem Th110: :: AOFA_L00:112

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 being Formula of L
for x, y being Element of Union X
for x0, y0 being Element of Union (X extended_by ({}, the carrier of S1)) st L is subst-correct holds
for a being SortSymbol of J st x in X . a & y in X . a & x0 = x & y0 = y holds
(A / (x0,y0)) \imp (\ex (x,A)) in G