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Theorem exinst01 33512
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  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  |-  E. x ps
exinst01.2  |-  (. ph ,. ps  ->.  ch ).
exinst01.3  |-  ( ph  ->  A. x ph )
exinst01.4  |-  ( ch 
->  A. x ch )
Assertion
Ref Expression
exinst01  |-  (. ph  ->.  ch
).

Proof of Theorem exinst01
StepHypRef Expression
1 exinst01.1 . . 3  |-  E. x ps
2 exinst01.2 . . . 4  |-  (. ph ,. ps  ->.  ch ).
32dfvd2i 33463 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
4 exinst01.3 . . 3  |-  ( ph  ->  A. x ph )
5 exinst01.4 . . 3  |-  ( ch 
->  A. x ch )
61, 3, 4, 5eexinst01 33397 . 2  |-  ( ph  ->  ch )
76dfvd1ir 33451 1  |-  (. ph  ->.  ch
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1393   E.wex 1613   (.wvd1 33447   (.wvd2 33455
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-nf 1618  df-vd1 33448  df-vd2 33456
This theorem is referenced by:  vk15.4jVD  33815
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