Theorem exbi 1870

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 23	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	alexbii 1856	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 209  ∀wal 1561  ∃wex 1802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832

This theorem depends on definitions:  df-bi 210  df-ex 1803

This theorem is referenced by:  exbii  1871  nfbiit  1874  19.19  2267  eubi  2614  axpr  5388  elirrv  9547  bj-2exbi  37081  bj-3exbi  37082  bj-hbyfrbi  37093  2exbi  44949  rexbidar  45014  onfrALTlem1VD  45457  csbxpgVD  45461  csbrngVD  45463  csbunigVD  45465  e2ebindVD  45479  e2ebindALT  45496