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Theorem exanOLD 1786
Description: Obsolete proof of exan 1785 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 474 . 2 𝑥𝜑
3 pm3.21 464 . . . 4 (𝜓 → (𝜑 → (𝜑𝜓)))
43aleximi 1756 . . 3 (∀𝑥𝜓 → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
51simpri 478 . . 3 𝜓
64, 5mpg 1721 . 2 (∃𝑥𝜑 → ∃𝑥(𝜑𝜓))
72, 6ax-mp 5 1 𝑥(𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702
This theorem is referenced by: (None)
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