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Theorem exinst 39166
Description: Existential Instantiation. Virtual deduction form of exlimexi 39047. (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 39118 . 2 (∃𝑥𝜑 → (𝜑𝜓))
41, 3exlimexi 39047 1 (∃𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521  wex 1744  (   wvd2 39110
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745  df-nf 1750  df-vd2 39111
This theorem is referenced by:  sb5ALTVD  39463
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