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Theorem exbi 1838
Description: Theorem 19.18 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
exbi (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Proof of Theorem exbi
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21alexbii 1824 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wal 1526  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801
This theorem depends on definitions:  df-bi 208  df-ex 1772
This theorem is referenced by:  exbii  1839  nfbiit  1842  19.19  2221  eubi  2662  bj-2exbi  33846  bj-3exbi  33847  bj-hbyfrbi  33861  2exbi  40589  rexbidar  40655  onfrALTlem1VD  41101  csbxpgVD  41105  csbrngVD  41107  csbunigVD  41109  e2ebindVD  41123  e2ebindALT  41140
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