Theorem bj-2exbi 34797

Description: Closed form of 2exbii 1851. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-2exbi	⊢ (∀𝑥∀𝑦(𝜑 ↔ 𝜓) → (∃𝑥∃𝑦𝜑 ↔ ∃𝑥∃𝑦𝜓))

Proof of Theorem bj-2exbi

Step	Hyp	Ref	Expression
1		exbi 1849	. 2 ⊢ (∀𝑦(𝜑 ↔ 𝜓) → (∃𝑦𝜑 ↔ ∃𝑦𝜓))
2	1	alexbii 1835	1 ⊢ (∀𝑥∀𝑦(𝜑 ↔ 𝜓) → (∃𝑥∃𝑦𝜑 ↔ ∃𝑥∃𝑦𝜓))

Syntax hints:   → wi 4   ↔ wb 205  ∀wal 1537  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by:  bj-3exbi  34798