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Theorem exinst01 27677
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 27637 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
4 exinst01.3 . . 3  |-  ( ph  ->  A. x ph )
5 exinst01.4 . . 3  |-  ( ch 
->  A. x ch )
61, 3, 4, 5eexinst01 27572 . 2  |-  ( ph  ->  ch )
76dfvd1ir 27624 1  |-  (. ph  ->.  ch
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528   (.wvd1 27620   (.wvd2 27629
This theorem is referenced by:  vk15.4jVD  27970
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-11 1716
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-vd1 27621  df-vd2 27630
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