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Theorem exintr 1895
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 545 . 2 ((𝜑𝜓) → (𝜑 → (𝜑𝜓)))
21aleximi 1834 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wal 1537  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783
This theorem is referenced by:  equs4v  2003  equs4  2416  eupickbi  2638  barbarilem  2669  ceqsex  3478  ceqsexv  3479  r19.2z  4425  pwpw0  4746  pwsnOLD  4832  bnj1023  32760  bnj1109  32766  pm10.55  41987
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