Theorem exbi 1854

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 1840	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 207  ∀wal 1545  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816

This theorem depends on definitions:  df-bi 208  df-ex 1787

This theorem is referenced by:  exbii  1855  nfbiit  1858  19.19  2241  eubi  2588  axpr  5363  elirrv  9509  bj-2exbi  36949  bj-3exbi  36950  bj-hbyfrbi  36961  2exbi  44831  rexbidar  44896  onfrALTlem1VD  45340  csbxpgVD  45344  csbrngVD  45346  csbunigVD  45348  e2ebindVD  45362  e2ebindALT  45379