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Theorem exinst 39374
Description: Existential Instantiation. Virtual deduction form of exlimexi 39255. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exinst.1 (𝜓 → ∀𝑥𝜓)
exinst.2 (   𝑥𝜑   ,   𝜑   ▶   𝜓   )
Assertion
Ref Expression
exinst (∃𝑥𝜑𝜓)

Proof of Theorem exinst
StepHypRef Expression
1 exinst.1 . 2 (𝜓 → ∀𝑥𝜓)
2 exinst.2 . . 3 (   𝑥𝜑   ,   𝜑   ▶   𝜓   )
32dfvd2i 39326 . 2 (∃𝑥𝜑 → (𝜑𝜓))
41, 3exlimexi 39255 1 (∃𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629  wex 1852  (   wvd2 39318
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853  df-nf 1858  df-vd2 39319
This theorem is referenced by:  sb5ALTVD  39671
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