let H be ZF-formula; :: thesis: for x, y being Variable st H is conditional holds
( the_antecedent_of (H / (x,y)) = (the_antecedent_of H) / (x,y) & the_consequent_of (H / (x,y)) = (the_consequent_of H) / (x,y) )
let x, y be Variable; :: thesis: ( H is conditional implies ( the_antecedent_of (H / (x,y)) = (the_antecedent_of H) / (x,y) & the_consequent_of (H / (x,y)) = (the_consequent_of H) / (x,y) ) )
assume A1: H is conditional ; :: thesis: ( the_antecedent_of (H / (x,y)) = (the_antecedent_of H) / (x,y) & the_consequent_of (H / (x,y)) = (the_consequent_of H) / (x,y) )
then H / (x,y) is conditional by Th175;
then A2: H / (x,y) = (the_antecedent_of (H / (x,y))) => (the_consequent_of (H / (x,y))) by ZF_LANG:47;
H = (the_antecedent_of H) => (the_consequent_of H) by A1, ZF_LANG:47;
hence ( the_antecedent_of (H / (x,y)) = (the_antecedent_of H) / (x,y) & the_consequent_of (H / (x,y)) = (the_consequent_of H) / (x,y) ) by A2, Th162; :: thesis: verum