Theorem exlimdh 2149

Description: Deduction form of Theorem 19.9 of [Margaris] p. 89. (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	1	nf5i 2024	. 2 |- F/ x ph
3		exlimdh.2	. . 3 |- ( ch -> A. x ch )
4	3	nf5i 2024	. 2 |- F/ x ch
5		exlimdh.3	. 2 |- ( ph -> ( ps -> ch ) )
6	2, 4, 5	exlimd 2087	1 |- ( ph -> ( E. x ps -> 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:  exlimexi  38730  eexinst01  38732  eexinst11  38733