Theorem exbi 1849

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 1835	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1540  ∃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 207  df-ex 1782

This theorem is referenced by:  exbii  1850  nfbiit  1853  19.19  2237  eubi  2585  axpr  5364  bj-2exbi  36912  bj-3exbi  36913  bj-hbyfrbi  36924  2exbi  44825  rexbidar  44890  onfrALTlem1VD  45334  csbxpgVD  45338  csbrngVD  45340  csbunigVD  45342  e2ebindVD  45356  e2ebindALT  45373