  Recently Jenei introduced a new structure called equality algebras which is
inspired by ideas of BCK-algebras with meet. These algebras were generalized by
Jenei and K\'or\'odi to pseudo equality algebras which are aimed to find a
connection with pseudo BCK-algebras with meet. We show that every pseudo
equality algebra is an equality algebra. Therefore, we define a new type of
pseudo equality algebras which more precisely reflects the relation to pseudo
BCK-algebras with meet in the sense of Kabzi\'nski and Wro\'nski. We describe
congruences via normal closed deductive systems, and we show that the variety
of pseudo equality algebras is subtractive, congruence distributive and
congruence permutable.
