Yes, you are right.
If we have a strong love in our hearts for God and all the creation of God then we would be automatically be keeping all the Ten Commandments mentioned in the Old Testament too. Because if we love our neighbours (our fellow-human beings) then we will not commit adultery, murder or robbery.
So, the first 2 Commandments help us to follow all the commandments as mentioned in Matthew 22:35-40 "Then one of them, which was a lawyer, asked him a question, tempting him, and saying, 36 Master, which is the great commandment in the law? 37 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. 38 This is the first and great commandment. 39 And the second is like unto it, Thou shalt love thy neighbour as thyself. 40 On these two commandments hang all the law and the prophets."
So as the last verse says, if we follow sincerely the two commandments mentioned in verse 37 and verse 39, then it is equal to following all the commandments and laws mentioned by the prophets.