Theorem exbi 1847

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 1833	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1538  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-ex 1780

This theorem is referenced by:  exbii  1848  nfbiit  1851  19.19  2230  eubi  2578  axpr  5385  bj-2exbi  36610  bj-3exbi  36611  bj-hbyfrbi  36626  2exbi  44376  rexbidar  44442  onfrALTlem1VD  44886  csbxpgVD  44890  csbrngVD  44892  csbunigVD  44894  e2ebindVD  44908  e2ebindALT  44925