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Metamath Proof Explorer

Theorem trut

Description: A proposition is equivalent to it being implied by T. . Closed form of mptru . Dual of dfnot . It is to tbtru what a1bi is to tbt . (Contributed by BJ, 26-Oct-2019)

		Ref	Expression
	Assertion	trut	$⊢ φ \leftrightarrow (⊤ \to φ)$

Proof

Step	Hyp	Ref	Expression
1		tru	$⊢ ⊤$
2	1	a1bi	$⊢ φ \leftrightarrow (⊤ \to φ)$