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Theorem exinst11 38671
Description: Existential Instantiation. Virtual Deduction rule corresponding to a special case of the Natural Deduction Sequent Calculus rule called Rule C in [Margaris] p. 79 and E in Table 1 on page 4 of the paper "Extracting information from intermediate T-systems" (2000) presented at IMLA99 by Mauro Ferrari, Camillo Fiorentini, and Pierangelo Miglioli. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exinst11.1 (   𝜑   ▶   𝑥𝜓   )
exinst11.2 (   𝜑   ,   𝜓   ▶   𝜒   )
exinst11.3 (𝜑 → ∀𝑥𝜑)
exinst11.4 (𝜒 → ∀𝑥𝜒)
Assertion
Ref Expression
exinst11 (   𝜑   ▶   𝜒   )

Proof of Theorem exinst11
StepHypRef Expression
1 exinst11.1 . . . 4 (   𝜑   ▶   𝑥𝜓   )
21in1 38607 . . 3 (𝜑 → ∃𝑥𝜓)
3 exinst11.2 . . . 4 (   𝜑   ,   𝜓   ▶   𝜒   )
43dfvd2i 38621 . . 3 (𝜑 → (𝜓𝜒))
5 exinst11.3 . . 3 (𝜑 → ∀𝑥𝜑)
6 exinst11.4 . . 3 (𝜒 → ∀𝑥𝜒)
72, 4, 5, 6eexinst11 38553 . 2 (𝜑𝜒)
87dfvd1ir 38609 1 (   𝜑   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1479  wex 1702  (   wvd1 38605  (   wvd2 38613
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-10 2017  ax-12 2045
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1703  df-nf 1708  df-vd1 38606  df-vd2 38614
This theorem is referenced by:  vk15.4jVD  38970
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