Under the First Mention principle, the idea is that God indicates the truth that stands in His mind that will not change later on. This means that the initial discussion of any subject in the Bible would have unusual significance by this standard, as Benjamin Willis Newton (a 19th century Plymouth Brethren member) observed.
Under the Progressive Principle, God declares His mind on the subject more clearly as His word moves towards its consummation. The Full or Complete Mention Principle concerns God's revealing His full truth on a given matter that is very important to our spiritual lives. J. Edwin Hartill's book, "Biblical Hermeneutics," would be a good source of more information on this subject.
An interesting application of the First mention hermeneutical principle comes from the verse discussing (if obliquely) the coming Savior and Messiah in Genesis 3:15. This verse is considered the first prophecy in the Bible.
15. And I will put enmity between you and the woman, and between your seed and her Seed; He will bruise your head, and you shall bruise His heel (Genesis 3:15, HBFV)
Later on, this theme develops in Genesis at length. It becomes clearer from the promise God made to Abraham to bless all families of the earth through him (Genesis 12:3, 26:4). God promised to use Abraham's "seed" to bless the world after he passed God's test to nearly sacrifice Isaac (Genesis 22:18). These would be progressive references of this theme.
In Galatians 3:8, 16, however, we find Paul's interpretation that the "seed" was a reference to Christ. Based on the first mention principle, this could be the consummation of what God obliquely promised in Genesis 3:15. Admittedly, there is some speculation here, for people can dispute concerning the interpretation of Old Testament Messianic texts.