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Theorem trujust 1476
Description: Soundness justification theorem for df-tru 1477. (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
StepHypRef Expression
1 id 22 . 2 (∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥)
2 id 22 . 2 (∀𝑦 𝑦 = 𝑦 → ∀𝑦 𝑦 = 𝑦)
31, 22th 252 1 ((∀𝑥 𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥) ↔ (∀𝑦 𝑦 = 𝑦 → ∀𝑦 𝑦 = 𝑦))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wal 1472   = wceq 1474
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 195
This theorem is referenced by: (None)
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