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Theorem exintr 1791
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 1789 . 2 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑𝜓)))
21biimpd 217 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wal 1472  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by:  equs4v  1880  equs4  2181  eupickbi  2431  ceqsex  3118  r19.2z  3915  pwpw0  4187  pwsnALT  4265  bnj1023  29951  bnj1109  29957  pm10.55  37472
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