theorem :: AOFA_000:65

for X being non empty disjoint_with_NAT set
for C1, C2, I1, I2, J1, J2 being Element of (FreeUnivAlgNSG (ECIW-signature,X)) st if-then-else (C1,I1,I2) = if-then-else (C2,J1,J2) holds
( C1 = C2 & I1 = J1 & I2 = J2 )