Talmud in Pesachim (117b) states:
צריך שיזכיר יציאת מצרים בקידוש היום
One must mention the exodus from Egypt during Kiddush. This is derived from Scripture.
I once saw a pilpul explanation from Rabbi Jonathon Eibuschutz. It is written that Jews were to be exiled for 400 years (counted from Isaac's birth), and a second verse states 430 years. What happened to the extra 30 years?
The decree was intended for the six days of the week only. Pharoah had them work on the Sabbath as well, which was 1/7th more than originally decreed. 1/7th of the 210 years of enslavement equals exactly 30 years. Thus the Sabbath was instrumental in allowing the Jews to leave Egyptian bondage earlier. Therefore it is mentioned in the Kiddush.
I think he means: Shabbat is an eternal day of rest. G-d's decree that Jews be subject to bondage therefore exempted Shabbat. It was due to this exemption that we go out early, since it was ignored by Pharoah. So it's another reason to thank G-d for the Shabbat.