Theorem exbi 1866

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 1852	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 208  ∀wal 1557  ∃wex 1798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828

This theorem depends on definitions:  df-bi 209  df-ex 1799

This theorem is referenced by:  exbii  1867  nfbiit  1870  19.19  2263  eubi  2610  axpr  5381  elirrv  9538  bj-2exbi  37034  bj-3exbi  37035  bj-hbyfrbi  37046  2exbi  44916  rexbidar  44981  onfrALTlem1VD  45425  csbxpgVD  45429  csbrngVD  45431  csbunigVD  45433  e2ebindVD  45447  e2ebindALT  45464