Theorem eexinst11 38733

Description: exinst11 38851 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
eexinst11.1	|- ( ph -> E. x ps )
eexinst11.2	|- ( ph -> ( ps -> ch ) )
eexinst11.3	|- ( ph -> A. x ph )
eexinst11.4	|- ( ch -> A. x ch )

Assertion

Ref	Expression
eexinst11	|- ( ph -> ch )

Proof of Theorem eexinst11

Step	Hyp	Ref	Expression
1		eexinst11.1	. . 3 |- ( ph -> E. x ps )
2		eexinst11.3	. . . 4 |- ( ph -> A. x ph )
3		eexinst11.4	. . . 4 |- ( ch -> A. x ch )
4		eexinst11.2	. . . 4 |- ( ph -> ( ps -> ch ) )
5	2, 3, 4	exlimdh 2149	. . 3 |- ( ph -> ( E. x ps -> ch ) )
6	1, 5	syl5com 31	. 2 |- ( ph -> ( ph -> ch ) )
7	6	pm2.43i 52	1 |- ( ph -> ch )

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

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-ex 1705  df-nf 1710

This theorem is referenced by:  vk15.4j  38734  exinst11  38851