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Theorem exan 1855
 Description: Place a conjunct in the scope of an existential quantifier. (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 shortened by Wolf Lammen, 6-Nov-2022.) Expand hypothesis. (Revised by Steven Nguyen, 19-Jun-2023.)
Hypotheses
Ref Expression
exan.1 𝑥𝜑
exan.2 𝜓
Assertion
Ref Expression
exan 𝑥(𝜑𝜓)

Proof of Theorem exan
StepHypRef Expression
1 exan.1 . 2 𝑥𝜑
2 exan.2 . . 3 𝜓
32jctr 525 . 2 (𝜑 → (𝜑𝜓))
41, 3eximii 1830 1 𝑥(𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 396  ∃wex 1773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803 This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1774 This theorem is referenced by:  sbtvOLD  2517  bm1.3ii  5203  ac6s6f  35338  fnchoice  41170
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