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Theorem exintr 1994
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 1993 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑𝜓)))
21biimpd 221 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386  wal 1654  wex 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879
This theorem is referenced by:  equs4v  2107  equs4  2436  eupickbi  2719  ceqsex  3458  r19.2z  4284  pwpw0  4564  pwsnALT  4653  bnj1023  31393  bnj1109  31399  pm10.55  39403
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