Distinction between the Three Religions
God did not destroy Judaism and Judaists 2000 years ago by sending Christ Jesus.
Although Judaists came into a state that disappointed God enough to send Christ Jesus to Israel, they were not wiped away. Christ Jesus did not even declare that Judaists should perish, while He said, "God is able of these stones to raise up children unto Abraham."
Rather, as Christianity expanded in Europe, Judaists expanded their presence in Europe. So, it seems that God had no intention to exterminate Judaists.
And, God did not destroy Christians by giving Islam to Arabs 1400 years ago. Rather God mentioned Christ Jesus in the Koran where Abraham and Moses were also mentioned. However, as the Vatican adopted a creed that Christ Jesus was God, God declared in the Koran that Christ Jesus was not God. Nonetheless, the emergence of Islam must have become a factor of pressure on the Vatican for strong self-control and governance against the rival religion Islam. As a result, both the religions, Christianity and Islam, have succeeded to maintain their order and avoid total corruption and collapse due to tense relations between them.
Since Islam is the latest religion God has given to mankind, we have to study its contents more carefully. There must be important messages in the Koran, although Muhammad might have some mistakes in copying holly messages into his own words or Satan might interfere.
Authenticity of Islam is based on its inclusion of Abraham, Moses, and Christ Jesus. If Islam had neglected these holy figures of Judaism and Christianity from the beginning, it might not have been accepted by Arabs and other tribes. Or Christians and Judaists in these 1400 years might have fully tried to destroy Islam as a harmful pagan religion.
Abraham in Islam
Ibrahim, known as Abraham in the Hebrew Bible, is recognized as a prophet and messenger in Islam  of God. Abraham plays a prominent role as an example of faith in Judaism, Christianity, and Islam. In Muslim belief, Abraham fulfilled all the commandments and trials wherein God nurtured him throughout his lifetime. As a result of his unwavering faith in God, Abraham was promised by God to be a leader to all the nations of the world. The Qur’an extols Abraham as a model, an exemplar, obedient and not an idolator.
Moses in Islam
Mûsâ al ibn Amram known as Moses in the Hebrew Bible, considered a prophet, messenger, and leader in Islam, is the most frequently mentioned individual in the Quran. In Islamic tradition, instead of introducing a new religion, Musa is regarded by Muslims as teaching and practicing the religion of his predecessors and confirming the scriptures and prophets before him. The Quran states that Moses was sent by God to the Pharaoh of Egypt and the Israelites for guidance and warning. Moses is mentioned more in the Quran than any other individual, and his life is narrated and recounted more than that of any other prophet.
Jesus in IslamHowever, the most important role of Islam might be emphasizing the relationship between the mankind and God through Abraham, Moses, and Christ Jesus. If so, ultimately distinction between the three religions, Judaism, Christianity, and Islam, should be abolished.
In Islam, Isa ibn Maryam, or Jesus, is understood to be the penultimate prophet and messenger of Allah (God) and al-Masih, the Arabic term for Messiah (Christ), sent to guide the Children of Israel (banī isrā'īl in Arabic) with a new revelation: al-Injīl (Arabic for "the Gospel"). Jesus is believed to be a prophet who neither married nor had any children and is reflected as a significant figure, being found in the Quran in 93 ayaat (Arabic for verses) with various titles attached such as "Son of Mary", "Spirit of God", and the "Word of God" among other relational terms, mentioned directly and indirectly, over 187 times. Jesus is the most mentioned person in the Quran; 25 times by the name Isa, 3rd-person 48 times, 1st-person 35 times, the rest as titles and attributes.
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Mat 5:28 But I say unto you, That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart.