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Theorem exinst01 41251
 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
exinst01.1 𝑥𝜓
exinst01.2 (   𝜑   ,   𝜓   ▶   𝜒   )
exinst01.3 (𝜑 → ∀𝑥𝜑)
exinst01.4 (𝜒 → ∀𝑥𝜒)
Assertion
Ref Expression
exinst01 (   𝜑   ▶   𝜒   )

Proof of Theorem exinst01
StepHypRef Expression
1 exinst01.1 . . 3 𝑥𝜓
2 exinst01.2 . . . 4 (   𝜑   ,   𝜓   ▶   𝜒   )
32dfvd2i 41211 . . 3 (𝜑 → (𝜓𝜒))
4 exinst01.3 . . 3 (𝜑 → ∀𝑥𝜑)
5 exinst01.4 . . 3 (𝜒 → ∀𝑥𝜒)
61, 3, 4, 5eexinst01 41152 . 2 (𝜑𝜒)
76dfvd1ir 41199 1 (   𝜑   ▶   𝜒   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  ∃wex 1781  (   wvd1 41195  (   wvd2 41203 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2146  ax-12 2179 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-vd1 41196  df-vd2 41204 This theorem is referenced by:  vk15.4jVD  41540
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