Theorem exlimexi 38730

Description: Inference similar to Theorem 19.23 of [Margaris] p. 90. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

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

Proof of Theorem exlimexi

Step	Hyp	Ref	Expression
1		hbe1 2021	. . 3 |- ( E. x ph -> A. x E. x ph )
2		exlimexi.1	. . 3 |- ( ps -> A. x ps )
3		exlimexi.2	. . 3 |- ( E. x ph -> ( ph -> ps ) )
4	1, 2, 3	exlimdh 2149	. 2 |- ( E. x ph -> ( E. x ph -> ps ) )
5	4	pm2.43i 52	1 |- ( E. x ph -> ps )

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:  sb5ALT  38731  exinst  38849