Theorem exbi 1848

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 1834	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1539  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810

This theorem depends on definitions:  df-bi 207  df-ex 1781

This theorem is referenced by:  exbii  1849  nfbiit  1852  19.19  2232  eubi  2579  axpr  5365  bj-2exbi  36655  bj-3exbi  36656  bj-hbyfrbi  36671  2exbi  44419  rexbidar  44484  onfrALTlem1VD  44928  csbxpgVD  44932  csbrngVD  44934  csbunigVD  44936  e2ebindVD  44950  e2ebindALT  44967