theorem Th14: :: ZFMODEL2:14

for x, y being Variable
for M being non empty set
for H being ZF-formula
for v being Function of VAR,M st not x. 0 in Free H & M,v |= All ((x. 3),(Ex ((x. 0),(All ((x. 4),(H <=> ((x. 4) '=' (x. 0)))))))) & not x in variables_in H & not y in Free H & x <> x. 0 & x <> x. 3 & x <> x. 4 holds
( not x. 0 in Free (H / (y,x)) & M,v / (x,(v . y)) |= All ((x. 3),(Ex ((x. 0),(All ((x. 4),((H / (y,x)) <=> ((x. 4) '=' (x. 0)))))))) & def_func' (H,v) = def_func' ((H / (y,x)),(v / (x,(v . y)))) )