 Taking it that the intention is clear for the general case what (RE′i) should be as a condition on consequence relations, we say that # is right-extensional according to ⊢ when (RE′i) is satisfied for each i up to the arity of #, and that # is extensional according to ⊢ just in case # is both left- and right-extensional according to ⊢. Then paralleling the above results for truth-functionality are the following for pseudo-truth-functionality: