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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	⊢ ( ∀ 𝑥 𝑥 = 𝑥 → ∀ 𝑥 𝑥 = 𝑥 )
2		df-tru	⊢ ( ⊤ ↔ ( ∀ 𝑥 𝑥 = 𝑥 → ∀ 𝑥 𝑥 = 𝑥 ) )
3	1 2	mpbir	⊢ ⊤