let H be ZF-formula; :: thesis: for x, y being Variable st H is biconditional holds
( the_left_side_of (H / x,y) = (the_left_side_of H) / x,y & the_right_side_of (H / x,y) = (the_right_side_of H) / x,y )
let x, y be Variable; :: thesis: ( H is biconditional implies ( the_left_side_of (H / x,y) = (the_left_side_of H) / x,y & the_right_side_of (H / x,y) = (the_right_side_of H) / x,y ) )
assume H is biconditional ; :: thesis: ( the_left_side_of (H / x,y) = (the_left_side_of H) / x,y & the_right_side_of (H / x,y) = (the_right_side_of H) / x,y )
then ( H / x,y is biconditional & H = (the_left_side_of H) <=> (the_right_side_of H) ) by Th190, ZF_LANG:67;
then ( H / x,y = (the_left_side_of (H / x,y)) <=> (the_right_side_of (H / x,y)) & H / x,y = ((the_left_side_of H) / x,y) <=> ((the_right_side_of H) / x,y) ) by Th177, ZF_LANG:67;
hence ( the_left_side_of (H / x,y) = (the_left_side_of H) / x,y & the_right_side_of (H / x,y) = (the_right_side_of H) / x,y ) by ZF_LANG:50; :: thesis: verum