Theorem trujust

Description: Soundness justification theorem for df-tru . Instance of monothetic . (Contributed by Mario Carneiro, 17-Nov-2013) (Revised by NM, 11-Jul-2019)

	Ref	Expression
Assertion	trujust	⊢ ( ( ∀ 𝑥 𝑥 = 𝑥 → ∀ 𝑥 𝑥 = 𝑥 ) ↔ ( ∀ 𝑦 𝑦 = 𝑦 → ∀ 𝑦 𝑦 = 𝑦 ) )

Proof

Step	Hyp	Ref	Expression
1		monothetic	⊢ ( ( ∀ 𝑥 𝑥 = 𝑥 → ∀ 𝑥 𝑥 = 𝑥 ) ↔ ( ∀ 𝑦 𝑦 = 𝑦 → ∀ 𝑦 𝑦 = 𝑦 ) )