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Theorem exinst11 28460
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 28395 . . 3  |-  ( ph  ->  E. x ps )
3 exinst11.2 . . . 4  |-  (. ph ,. ps  ->.  ch ).
43dfvd2i 28410 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
5 exinst11.3 . . 3  |-  ( ph  ->  A. x ph )
6 exinst11.4 . . 3  |-  ( ch 
->  A. x ch )
72, 4, 5, 6eexinst11 28346 . 2  |-  ( ph  ->  ch )
87dfvd1ir 28397 1  |-  (. ph  ->.  ch
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1529   E.wex 1530   (.wvd1 28393   (.wvd2 28402
This theorem is referenced by:  vk15.4jVD  28763
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-11 1717
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1531  df-nf 1534  df-vd1 28394  df-vd2 28403
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