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 209  ∀wal 1536  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 210  df-ex 1782

This theorem is referenced by:  exbii  1849  nfbiit  1852  19.19  2229  eubi  2644  bj-2exbi  34062  bj-3exbi  34063  bj-hbyfrbi  34077  2exbi  41084  rexbidar  41150  onfrALTlem1VD  41596  csbxpgVD  41600  csbrngVD  41602  csbunigVD  41604  e2ebindVD  41618  e2ebindALT  41635