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Theorem 19.25 1949
Description: Theorem 19.25 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
19.25 (∀𝑦𝑥(𝜑𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))

Proof of Theorem 19.25
StepHypRef Expression
1 19.35 1946 . . 3 (∃𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
21biimpi 206 . 2 (∃𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∃𝑥𝜓))
32aleximi 1900 1 (∀𝑦𝑥(𝜑𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1622  wex 1845
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878
This theorem depends on definitions:  df-bi 197  df-ex 1846
This theorem is referenced by: (None)
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