theorem :: AOFA_L00:150

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 x, y being Element of Union X
for x0, y0 being Element of Union (X extended_by ({}, the carrier of S1))
for L being non-empty Language of X extended_by ({}, the carrier of S1),S1
for G1 being QC-theory_with_equality of L
for A being Formula of L
for s being SortSymbol of S1 st L is subst-correct3 & L is vf-finite & L is subst-correct2 & L is subst-correct & L is subst-eq-correct & L is vf-qc-correct & L is vf-eq-correct & x = x0 & x0 in X . s & y = y0 & y0 in X . s & x <> y & y nin (vf A) . s & X . s is infinite holds
\for (x,(A \iff (\for (y,((x '=' (y,L)) \imp (A / (x0,y0))))))) in G1