How can Ammonia be a base since it lakes a hydroxide ion? thank you so much

Ammonia, NH3, reacts with water, H2O, as follows:

NH3 + HOH ==> NH4^+ + OH^-
Note that NH3 has pulled a H^+ away from HOH (water, H2O) to form the ammonium ion, (NH4^+), leaving the OH^- alone. So we now have NH4^+ and OH^- floating around from the reaction, plus H^+ and OH^- from the water, plus unionized H2O plus unreacted NH3.