It is so evident from the clear and frequent testimonies of holy writ that the true Church of Jesus Christ is one, that no Christian can dare to deny it. But in judging and determining the nature of this unity many have erred in various ways. Not the foundation of the Church alone, but its whole constitution, belongs to the class of things effected by Christ’s free choice. For this reason the entire case must be judged by what was actually done. We must consequently investigate not how the Church may possibly be one, but how He, who founded it, willed that it should be one.
But when we consider what was actually done we find that Jesus Christ did not, in point of fact, institute a Church to embrace several communities similar in nature, but in themselves distinct, and lacking those bonds which render the Church unique and indivisible after that manner in which in the symbol of our faith we profess: “I believe in one Church.”
“The Church in respect of its unity belongs to the category of things indivisible by nature, though heretics try to divide it into many parts….We say, therefore, that the Catholic Church is unique in its essence, in its doctrine, in its origin, and in its excellence….Furthermore, the eminence of the Church arises from its unity, as the principle of its constitution–a unity surpassing all else, and having nothing like unto it or equal to it.” For this reason Christ, speaking of the mystical edifice, mentions only one Church, which He calls His own–”I will build My church”; any other Church except this one, since it has not been founded by Christ, cannot be the true Church. This becomes even more evident when the purpose of the divine Founder is considered. For what did Christ, the Lord, ask? What did He wish in regard to the Church founded, or about to be founded? This: to transmit to it the same mission and the same mandate which He had received from the Father, they they should be perpetuated. This he clearly resolved to do: this He actually did. “As the Father hath sent me, I also send you.”  “As thou hast sent Me into the world I also have sent them into the world.” 
But the mission of Christ is to save “that which had perished”; that is to say, not some nations or peoples, but the whole human race, without distinction of time or place. “The Son of Man came that the world might be saved by Him.”  “For there is no other name under heaven given to men whereby we must be saved.”  The Church, therefore, is bound to communicate without stint to all men, and to transmit through all ages, the salvation effected by Jesus Christ, and the blessings flowing therefrom. Wherefore, by the will of its Founder, it is necessary that this Church should be one in all lands and at all times. To justify the existence of more than one Church it would be necessary to go outside this world, and to create a new and unheard-of race of men.
-Pope Leo XIII, Satis Cognitum, 11-14
 St. Clemens Alexandrinus, Stromatum, lib. viii., c.17.
 John 20:21
 John 17:18
 John 3:17
 Acts 4:12