Theorem trujust 1345

Description: Soundness justification theorem for df-tru 1346. (Contributed by Mario Carneiro, 17-Nov-2013.) (Revised by NM, 11-Jul-2019.)

Assertion

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

Proof of Theorem trujust

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥)
2		id 19	. 2 ⊢ (∀𝑦 𝑦 = 𝑦 → ∀𝑦 𝑦 = 𝑦)
3	1, 2	2th 173	1 ⊢ ((∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥) ↔ (∀𝑦 𝑦 = 𝑦 → ∀𝑦 𝑦 = 𝑦))

Syntax hints:   → wi 4   ↔ wb 104  ∀wal 1341   = wceq 1343

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)