לרפאות שרה חאנטשא בת אהבה נחמה
In our bentching we apparently repeat the same idea - ועל שהוצאתנו השם א-להנו מארץ מצרים ופדיתנו מבית עבדים - We thank Hashem for taking us out of Egypt and redeeming us from the house of slavery. Why the repetition?
Egypt is a physical place but not one where we would want to be. We are very thankful that we are no longer there. When we were there we suffered great physical and spiritual anguish being enslaved by the evil, cruel and idolatrous Egyptians. So first we thank Hashem for not being in the physical Egypt and then thank Him for not being enslaved. [עי' שפת אמת וארא תרל"א ובאר משה לצדיק מאוז'ורוב זצ"ל שמות עמ' שלג-ד].
The more we appreciate Hashem's kindness in taking us out, the more we can serve Him with joy.
What is interesting is that the gemara NEVER MENTIONS that we must mention yetzis mitzraim in bentching! In fact, Rav Amram Gaon, in his siddur found in the Cairo Geniza, omits any mention of it. The Magen Avraham [סימן קצ"ב] also omits it. Some suggest that since in vidui bikkurim, where we thank Hashem for the fruits, we thank Hashm for yetzias mitzraim, we also mention it here. [עי' בס' ברכת דוד עמ' קמ"א].