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Metamath Proof Explorer

Theorem tru

Description: The truth value T. is provable. (Contributed by Anthony Hart, 13-Oct-2010)

		Ref	Expression
	Assertion	tru	$⊢ ⊤$

Step	Hyp	Ref	Expression
1		id	$⊢ \forall x x = x \to \forall x x = x$
2		df-tru	$⊢ ⊤ \leftrightarrow (\forall x x = x \to \forall x x = x)$
3	1 2	mpbir	$⊢ ⊤$