Name two ideas in that declaration of independence that are still part of the main beliefs of our country's

1) Quote from the Declaration:
"We hold these truths to be self-evident, that all men are created equal"

This idea, of equality is still present, and extend to women as well (and to people of colour which were not meant at the time).

2) Quote from the Declaration:
"That whenever [Government is abusive, people can choose a new government ] , as to them shall seem most likely to effect their Safety and Happiness"

This idea, of equality is still present: all people have the right to pursue safety and happiness.