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Theorem exinst11 33145
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
exinst11.1  |-  (. ph  ->.  E. x ps ).
exinst11.2  |-  (. ph ,. ps  ->.  ch ).
exinst11.3  |-  ( ph  ->  A. x ph )
exinst11.4  |-  ( ch 
->  A. x ch )
Assertion
Ref Expression
exinst11  |-  (. ph  ->.  ch
).

Proof of Theorem exinst11
StepHypRef Expression
1 exinst11.1 . . . 4  |-  (. ph  ->.  E. x ps ).
21in1 33081 . . 3  |-  ( ph  ->  E. x ps )
3 exinst11.2 . . . 4  |-  (. ph ,. ps  ->.  ch ).
43dfvd2i 33095 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
5 exinst11.3 . . 3  |-  ( ph  ->  A. x ph )
6 exinst11.4 . . 3  |-  ( ch 
->  A. x ch )
72, 4, 5, 6eexinst11 33030 . 2  |-  ( ph  ->  ch )
87dfvd1ir 33083 1  |-  (. ph  ->.  ch
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1381   E.wex 1599   (.wvd1 33079   (.wvd2 33087
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-12 1840
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1600  df-nf 1604  df-vd1 33080  df-vd2 33088
This theorem is referenced by:  vk15.4jVD  33447
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