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God appeared onto Isaac to make the blessing personal. Isaac received the blessing for Abraham's sake. It was Abraham's faith that secured a blessing for his son. God says that he visits the sins of the father onto the third and fourth generation, but also blesses the children of the righteous for many generations.

I am sure that Abraham's life and example influenced Isaac greatly. I mean after all the whole sacrifice thing must have made some kind of impression on him. But the physical blessings and protection that Isaac enjoyed were the direct result of his father's faith. I hope that the faith of my husband and I will have similar results on my children. So far, so good.