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Theorem 2exim 39418
Description: Theorem *11.34 in [WhiteheadRussell] p. 162. Theorem 19.22 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2exim (∀𝑥𝑦(𝜑𝜓) → (∃𝑥𝑦𝜑 → ∃𝑥𝑦𝜓))

Proof of Theorem 2exim
StepHypRef Expression
1 exim 1934 . 2 (∀𝑦(𝜑𝜓) → (∃𝑦𝜑 → ∃𝑦𝜓))
21aleximi 1932 1 (∀𝑥𝑦(𝜑𝜓) → (∃𝑥𝑦𝜑 → ∃𝑥𝑦𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1656  wex 1880
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910
This theorem depends on definitions:  df-bi 199  df-ex 1881
This theorem is referenced by: (None)
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