Theorem exinst 38849

Description: Existential Instantiation. Virtual deduction form of exlimexi 38730. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
exinst.1	|- ( ps -> A. x ps )
exinst.2	|- (. E. x ph ,. ph ->. ps ).

Assertion

Ref	Expression
exinst	|- ( E. x ph -> ps )

Proof of Theorem exinst

Step	Hyp	Ref	Expression
1		exinst.1	. 2 |- ( ps -> A. x ps )
2		exinst.2	. . 3 |- (. E. x ph ,. ph ->. ps ).
3	2	dfvd2i 38801	. 2 |- ( E. x ph -> ( ph -> ps ) )
4	1, 3	exlimexi 38730	1 |- ( E. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704   (.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-vd2 38794

This theorem is referenced by:  sb5ALTVD  39149