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Theorem exbi 1848
 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 1834 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209  ∀wal 1536  ∃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 210  df-ex 1782 This theorem is referenced by:  exbii  1849  nfbiit  1852  19.19  2232  eubi  2668  bj-2exbi  34023  bj-3exbi  34024  bj-hbyfrbi  34038  2exbi  41022  rexbidar  41088  onfrALTlem1VD  41534  csbxpgVD  41538  csbrngVD  41540  csbunigVD  41542  e2ebindVD  41556  e2ebindALT  41573
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