let H be ZF-formula; :: thesis: ( H is conditional implies the_consequent_of H = the_argument_of (the_right_argument_of (the_argument_of H)) )
assume H is conditional ; :: thesis: the_consequent_of H = the_argument_of (the_right_argument_of (the_argument_of H))
then H = (the_antecedent_of H) => (the_consequent_of H) by ZF_LANG:47;
then the_argument_of H = (the_antecedent_of H) '&' ('not' (the_consequent_of H)) by Th3;
then the_right_argument_of (the_argument_of H) = 'not' (the_consequent_of H) by Th4;
hence the_consequent_of H = the_argument_of (the_right_argument_of (the_argument_of H)) by Th3; :: thesis: verum