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Theorem exinst01 39375
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 39326 . . 3 (𝜑 → (𝜓𝜒))
4 exinst01.3 . . 3 (𝜑 → ∀𝑥𝜑)
5 exinst01.4 . . 3 (𝜒 → ∀𝑥𝜒)
61, 3, 4, 5eexinst01 39257 . 2 (𝜑𝜒)
76dfvd1ir 39314 1 (   𝜑   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629  wex 1852  (   wvd1 39310  (   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-vd1 39311  df-vd2 39319
This theorem is referenced by:  vk15.4jVD  39672
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