Theorem tru

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

	Ref	Expression
Assertion	tru	⊢ ⊤

Proof

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	⊢ ⊤