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Theorem exintr 1886
 Description: Introduce a conjunct in the scope of an existential quantifier. (Contributed by NM, 11-Aug-1993.) (Proof shortened by BJ, 16-Sep-2022.)
Assertion
Ref Expression
exintr (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))

Proof of Theorem exintr
StepHypRef Expression
1 ancl 547 . 2 ((𝜑𝜓) → (𝜑 → (𝜑𝜓)))
21aleximi 1825 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 398  ∀wal 1528  ∃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 209  df-an 399  df-ex 1774 This theorem is referenced by:  equs4v  1999  equs4  2431  eupickbi  2715  barbarilem  2749  ceqsex  3539  r19.2z  4438  pwpw0  4738  pwsnALT  4823  bnj1023  32040  bnj1109  32046  pm10.55  40681
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