Theorem trujust 1541

Description: Soundness justification theorem for df-tru 1542. Instance of monothetic 265. (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		monothetic 265	1 ⊢ ((∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥) ↔ (∀𝑦 𝑦 = 𝑦 → ∀𝑦 𝑦 = 𝑦))

Syntax hints:   → wi 4   ↔ wb 205  ∀wal 1537   = wceq 1539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206

This theorem is referenced by: (None)