let H be ZF-formula; :: thesis: ( H is conditional implies ( H is negative & the_argument_of H is conjunctive & the_right_argument_of (the_argument_of H) is negative ) )
assume H is conditional ; :: thesis: ( H is negative & the_argument_of H is conjunctive & the_right_argument_of (the_argument_of H) is negative )
then A1: H = (the_antecedent_of H) => (the_consequent_of H) by ZF_LANG:47;
hence H is negative ; :: thesis: ( the_argument_of H is conjunctive & the_right_argument_of (the_argument_of H) is negative )
A2: the_argument_of H = (the_antecedent_of H) '&' ('not' (the_consequent_of H)) by A1, Th3;
hence the_argument_of H is conjunctive ; :: thesis: the_right_argument_of (the_argument_of H) is negative
the_right_argument_of (the_argument_of H) = 'not' (the_consequent_of H) by A2, Th4;
hence the_right_argument_of (the_argument_of H) is negative ; :: thesis: verum