This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem dftru2

Description: An alternate definition of "true" (see comment of df-tru ). The associated justification theorem is monothetic . (Contributed by Anthony Hart, 13-Oct-2010) (Revised by BJ, 12-Jul-2019) Use tru instead. (New usage is discouraged.)

		Ref	Expression
	Assertion	dftru2	$⊢ ⊤ \leftrightarrow (φ \to φ)$

Proof

Step	Hyp	Ref	Expression
1		tru	$⊢ ⊤$
2		id	$⊢ φ \to φ$
3	1 2	2th	$⊢ ⊤ \leftrightarrow (φ \to φ)$