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Theorem exbi 1762
 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 1750 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195  ∀wal 1473  ∃wex 1695 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728 This theorem depends on definitions:  df-bi 196  df-ex 1696 This theorem is referenced by:  exbii  1764  exbidhOLD  1782  exintrbiOLD  1809  19.19  2084  bnj956  30101  bj-2exbi  31784  bj-3exbi  31785  bj-nfbi  31793  bj-nfbiit  32024  2exbi  37601  rexbidar  37671  onfrALTlem5VD  38143  onfrALTlem1VD  38148  csbxpgVD  38152  csbrngVD  38154  csbunigVD  38156  e2ebindVD  38170  e2ebindALT  38187
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