Theorem exinst11 38851

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

Step	Hyp	Ref	Expression
1		exinst11.1	. . . 4 |- (. ph ->. E. x ps ).
2	1	in1 38787	. . 3 |- ( ph -> E. x ps )
3		exinst11.2	. . . 4 |- (. ph ,. ps ->. ch ).
4	3	dfvd2i 38801	. . 3 |- ( ph -> ( ps -> ch ) )
5		exinst11.3	. . 3 |- ( ph -> A. x ph )
6		exinst11.4	. . 3 |- ( ch -> A. x ch )
7	2, 4, 5, 6	eexinst11 38733	. 2 |- ( ph -> ch )
8	7	dfvd1ir 38789	1 |- (. ph ->. ch ).

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704   (.wvd1 38785   (.wvd2 38793

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710  df-vd1 38786  df-vd2 38794

This theorem is referenced by:  vk15.4jVD  39150