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Theorem exintr 1887
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 543 . 2 ((𝜑𝜓) → (𝜑 → (𝜑𝜓)))
21aleximi 1826 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394  wal 1531  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 206  df-an 395  df-ex 1774
This theorem is referenced by:  equs4v  1995  equs4  2409  eupickbi  2624  barbarilem  2656  ceqsexOLD  3513  ceqsexvOLD  3515  r19.2z  4496  pwpw0  4818  bnj1023  34542  bnj1109  34548  pm10.55  43948
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