let H be ZF-formula; :: thesis: ( H is existential implies ( H is negative & the_argument_of H is universal & the_scope_of (the_argument_of H) is negative ) )
assume H is existential ; :: thesis: ( H is negative & the_argument_of H is universal & the_scope_of (the_argument_of H) is negative )
then A1: H = Ex ((bound_in H),(the_scope_of H)) by ZF_LANG:45;
hence H is negative ; :: thesis: ( the_argument_of H is universal & the_scope_of (the_argument_of H) is negative )
A2: the_argument_of H = All ((bound_in H),('not' (the_scope_of H))) by A1, Th3;
hence the_argument_of H is universal ; :: thesis: the_scope_of (the_argument_of H) is negative
'not' (the_scope_of H) = the_scope_of (the_argument_of H) by A2, Th8;
hence the_scope_of (the_argument_of H) is negative ; :: thesis: verum