for M being non empty set
for H, H1, H2 being ZF-formula
for v being Function of VAR,M st {(x. 0),(x. 1),(x. 2)} misses Free H1 & M,v |= All ((x. 3),(Ex ((x. 0),(All ((x. 4),(H1 <=> ((x. 4) '=' (x. 0)))))))) & {(x. 0),(x. 1),(x. 2)} misses Free H2 & M,v |= All ((x. 3),(Ex ((x. 0),(All ((x. 4),(H2 <=> ((x. 4) '=' (x. 0)))))))) & {(x. 0),(x. 1),(x. 2)} misses Free H & not x. 4 in Free H holds
for FG being Function st dom FG = M & ( for m being Element of M holds
( ( M,v / ((x. 3),m) |= H implies FG . m = (def_func' (H1,v)) . m ) & ( M,v / ((x. 3),m) |= 'not' H implies FG . m = (def_func' (H2,v)) . m ) ) ) holds
FG is_parametrically_definable_in M