Theorem bj-dvv 37400

Description: A special instance of bj-hbaeb2 37397. 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 ↔ ∀𝑥∀𝑦 𝑥 = 𝑦)

Proof of Theorem bj-dvv

Step	Hyp	Ref	Expression
1		bj-hbaeb2 37397	1 ⊢ (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥∀𝑦 𝑥 = 𝑦)

Syntax hints:   ↔ wb 209  ∀wal 1566

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-10 2174  ax-12 2211  ax-13 2402

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1571  df-ex 1808  df-nf 1812

This theorem is referenced by: (None)