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Theorem exintr 1899
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 548 . 2 ((𝜑𝜓) → (𝜑 → (𝜑𝜓)))
21aleximi 1838 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wal 1540  wex 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787
This theorem is referenced by:  equs4v  2011  equs4  2416  eupickbi  2639  barbarilem  2670  ceqsex  3444  r19.2z  4381  pwpw0  4701  pwsnOLD  4789  bnj1023  32331  bnj1109  32337  pm10.55  41525
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