Theorem exlimdh 1589

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jan-1997.)

Hypotheses

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

Assertion

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

Proof of Theorem exlimdh

Step	Hyp	Ref	Expression
1		exlimdh.1	. . 3 |- ( ph -> A. x ph )
2		exlimdh.3	. . 3 |- ( ph -> ( ps -> ch ) )
3	1, 2	alrimih 1462	. 2 |- ( ph -> A. x ( ps -> ch ) )
4		exlimdh.2	. . 3 |- ( ch -> A. x ch )
5	4	19.23h 1491	. 2 |- ( A. x ( ps -> ch ) <-> ( E. x ps -> ch ) )
6	3, 5	sylib 121	1 |- ( ph -> ( E. x ps -> ch ) )

Syntax hints:   -> wi 4   A.wal 1346   E.wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1440  ax-gen 1442  ax-ie2 1487

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exlimd  1590  exim  1592  exlimdv  1812  equs5  1822  cbvexdh  1919  exists2  2116