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Theorem exintr 1932
Description: Introduce a conjunct in the scope of an existential quantifier. (Contributed by NM, 11-Aug-1993.)
Assertion
Ref Expression
exintr (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))

Proof of Theorem exintr
StepHypRef Expression
1 exintrbi 1931 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑𝜓)))
21biimpd 219 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wal 1594  wex 1817
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1818
This theorem is referenced by:  equs4v  2049  equs4  2399  eupickbi  2641  ceqsex  3345  r19.2z  4168  pwpw0  4452  pwsnALT  4537  bnj1023  31079  bnj1109  31085  pm10.55  38987
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