Is the phrase "Praise be to Allah for the existence of Allah" (الحمد لله على وجود الله) of legitimate origin, and is it permissible to say it?

It appears that the intent of the one who says "Praise be to Allah, Allah exists" is to evoke hope in the heart. For instance, it might be said to someone afflicted: "Praise be to Allah, Allah exists," meaning that He will have mercy on you and compensate you. And to the oppressed: "Allah exists," meaning that He knows your injustice and it will not be lost. There is no harm in this statement, as it is permissible to state something about Allah Almighty and intend a necessary implication thereof, as in His statement to Moses and Aaron: ﴿Fear not; verily I am with you both, hearing and seeing.﴾ (Qur'an 20:46). Better still is for the intent to be: Praise be to Allah that we have a Lord Whom we worship, Whose divinity has enriched us from needing anyone else, and praise be to Him for guiding us. If this is the intent of the speaker, then there is no harm in the expression. However, it is better to adhere to the wording that has been transmitted and the guidance of the Prophet (peace be upon him), as the narrated forms of praise are suitable for the context in which they were said. And if a servant says "Praise be to Allah" and stops, it would suffice and fulfill the purpose, for "Praise be to Allah fills the scale."