let H be ZF-formula; :: thesis: ( H is disjunctive implies the_left_argument_of H = the_argument_of (the_left_argument_of (the_argument_of H)) )
assume H is disjunctive ; :: thesis: the_left_argument_of H = the_argument_of (the_left_argument_of (the_argument_of H))
then H = (the_left_argument_of H) 'or' (the_right_argument_of H) by ZF_LANG:41;
then the_argument_of H = ('not' (the_left_argument_of H)) '&' ('not' (the_right_argument_of H)) by Th3;
then the_left_argument_of (the_argument_of H) = 'not' (the_left_argument_of H) by Th4;
hence the_left_argument_of H = the_argument_of (the_left_argument_of (the_argument_of H)) by Th3; :: thesis: verum