Theorem exbi 1857

Description: Theorem 19.18 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Assertion

Ref	Expression
exbi	⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Proof of Theorem exbi

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	alexbii 1843	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 208  ∀wal 1548  ∃wex 1789

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1805  ax-4 1819

This theorem depends on definitions:  df-bi 209  df-ex 1790

This theorem is referenced by:  exbii  1858  nfbiit  1861  19.19  2254  eubi  2601  axpr  5374  elirrv  9531  bj-2exbi  37012  bj-3exbi  37013  bj-hbyfrbi  37024  2exbi  44894  rexbidar  44959  onfrALTlem1VD  45403  csbxpgVD  45407  csbrngVD  45409  csbunigVD  45411  e2ebindVD  45425  e2ebindALT  45442