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Theorem bj-dvv 34624
Description: A special instance of bj-hbaeb2 34621. A lemma for distinct var metavariables. Note that the right-hand side is a closed formula (a sentence). (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-dvv (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥𝑦 𝑥 = 𝑦)

Proof of Theorem bj-dvv
StepHypRef Expression
1 bj-hbaeb2 34621 1 (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥𝑦 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-10 2144  ax-12 2178  ax-13 2371
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-ex 1787  df-nf 1791
This theorem is referenced by: (None)
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