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Theorem exanOLD 1776
 Description: Obsolete proof of exan 1775 as of 8-Oct-2021. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) Reduce axiom dependencies. (Revised by BJ, 7-Jul-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
exan.1 (∃𝑥𝜑𝜓)
Assertion
Ref Expression
exanOLD 𝑥(𝜑𝜓)

Proof of Theorem exanOLD
StepHypRef Expression
1 exan.1 . . 3 (∃𝑥𝜑𝜓)
21simpli 473 . 2 𝑥𝜑
3 pm3.21 463 . . . 4 (𝜓 → (𝜑 → (𝜑𝜓)))
43aleximi 1749 . . 3 (∀𝑥𝜓 → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
51simpri 477 . . 3 𝜓
64, 5mpg 1715 . 2 (∃𝑥𝜑 → ∃𝑥(𝜑𝜓))
72, 6ax-mp 5 1 𝑥(𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  ∃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-an 385  df-ex 1696 This theorem is referenced by: (None)
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